Bài tập c++ ​​tìm kiếm nhị phân

Vấn đề. Cho một mảng đã được sắp xếp arr[] gồm n phần tử, hãy viết hàm tìm kiếm phần tử x đã cho trong mảng[] và trả về chỉ số của x trong mảng

Show

    Coi mảng là 0 chỉ số cơ sở

    ví dụ.  

    Đầu vào. mảng[] = {10, 20, 30, 50, 60, 80, 110, 130, 140, 170}, x = 110
    Đầu ra. 6
    Giải thích. Yếu tố x có mặt tại chỉ số 6.

    Đầu vào. mảng[] = {10, 20, 30, 40, 60, 110, 120, 130, 170}, x = 175
    Đầu ra. -1
    Giải thích. Phần tử x không có trong arr[].

    Phương pháp tìm kiếm tuyến tính. Một cách tiếp cận đơn giản là thực hiện tìm kiếm tuyến tính. Độ phức tạp thời gian của tìm kiếm tuyến tính là O(n). Một cách tiếp cận khác để thực hiện nhiệm vụ tương tự là sử dụng Tìm kiếm nhị phân.   

    Phương pháp tìm kiếm nhị phân.  

    Tìm kiếm nhị phân là một thuật toán tìm kiếm được sử dụng trong một mảng được sắp xếp bằng cách chia đôi khoảng thời gian tìm kiếm nhiều lần. Ý tưởng của tìm kiếm nhị phân là sử dụng thông tin mà mảng được sắp xếp và giảm độ phức tạp về thời gian xuống O(Log n).  

    Thuật toán tìm kiếm nhị phân. Các bước cơ bản để thực hiện Tìm kiếm nhị phân là

    • Bắt đầu với phần tử giữa của toàn bộ mảng làm khóa tìm kiếm
    • Nếu giá trị của khóa tìm kiếm bằng với mục thì trả về chỉ mục của khóa tìm kiếm
    • Hoặc nếu giá trị của khóa tìm kiếm nhỏ hơn mục ở giữa khoảng thời gian, hãy thu hẹp khoảng thời gian xuống nửa dưới
    • Nếu không, hãy thu hẹp nó ở nửa trên
    • Kiểm tra liên tục từ điểm thứ hai cho đến khi tìm thấy giá trị hoặc khoảng trống

    Thuật toán tìm kiếm nhị phân có thể được thực hiện theo hai cách sau

    1. Phương pháp lặp
    2. Phương pháp đệ quy

    1. Phương pháp lặp

        binarySearch(arr, x, low, high)
            repeat till low = high
                   mid = (low + high)/2
                       if (x == arr[mid])
                       return mid
       
                       else if (x > arr[mid]) // x is on the right side
                           low = mid + 1
       
                       else                  // x is on the left side
                           high = mid - 1

    2. Phương pháp đệ quy (Phương pháp đệ quy theo phương pháp chia để trị)

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 

    Minh họa thuật toán tìm kiếm nhị phân.  

    Bài tập c++ ​​tìm kiếm nhị phân

    Ví dụ về thuật toán tìm kiếm nhị phân

    Đề nghị thực hành

    Tìm kiếm nhị phân

    Thử nó

    Bài tập c++ ​​tìm kiếm nhị phân

    Thuật toán tìm kiếm nhị phân từng bước. Về cơ bản, chúng tôi bỏ qua một nửa số yếu tố chỉ sau một lần so sánh

    1. So sánh x với phần tử ở giữa
    2. Nếu x khớp với phần tử ở giữa, chúng tôi trả về chỉ số giữa
    3. Khác Nếu x lớn hơn phần tử ở giữa thì x chỉ có thể nằm ở nửa mảng con bên phải sau phần tử ở giữa. Vì vậy, chúng tôi lặp lại cho một nửa bên phải
    4. Khác (x nhỏ hơn) lặp lại cho nửa bên trái

    Thực hiện đệ quy tìm kiếm nhị phân

    C++




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    494

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    495

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    497
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    498

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    0

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    1

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    31

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    33

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4950

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____14952

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4958____14959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4964

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4970
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4972
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4974

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4977

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4979

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4981
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4984
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4985
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4986

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4989

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    C




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    01

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    02

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    0

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    1

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    31

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    33

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4950

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____14952

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4958____14959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4964

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4970
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4972
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4974

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4977

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4979

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    84____185
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    85
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    93
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    94

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4989

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    Java




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    99

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    201

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    205

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    224
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    228

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    230

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    246
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    248

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    255____1247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    257

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    261

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    263

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266____1247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    272

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    277

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    281______1282
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    283

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    286
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    296

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    299

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    302____1293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    307____2308
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    309
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    248

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    314
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    319
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    325

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    327

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    331

    Python3




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    332

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    333

     

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    335

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____2337

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    340
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    342

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    346
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    348
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    350
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____2355

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    358
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    361

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____2366

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    368

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    370
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    371

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    374
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    377

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____2379

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____2381

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322____190

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    387
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    390

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____2395

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266____1247

     

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    201
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    213

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    214
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    217

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    218
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    220
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    308
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    223
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    224
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    377

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    229____2341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    237
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    238
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    239

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

    C#




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    249

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    251

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    253

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    255

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    261
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    228

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    230

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    261

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    263

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    272

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49420

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

     

    _______127____13____149425

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49428

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4977

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4979

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    319
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    325

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49447____2327

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49452

    PHP




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49453

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49454

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49455

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49456

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49457

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49458

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49459

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49460
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4_______149462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49474
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49481
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49484
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49488

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149490

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149492

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49499
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49504
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149509

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149511

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149513

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49520
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49530
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49532
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149536

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149538

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49479
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49545

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49546
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49552

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49553

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49557

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341____149560
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49561

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49562
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49564
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49569

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49570
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49571____149462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49573
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49562
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49532
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49579
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49570
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49581

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49582
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49582
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4985____1288

    _______149546____149570____1226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49546

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49593

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49594

    Javascript




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49595

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49596

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    0

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    1

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49460
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49601

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149606

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    31

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    33

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    29

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4950

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____14952

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49644

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49645

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49646

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49647

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49648
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49651
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49652____14985
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49654

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49655

    Đầu ra

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

    Độ phức tạp về thời gian. O(log n)
    Không gian phụ. O(log n)

    Một cách tiếp cận lặp lại khác để tìm kiếm nhị phân

    C++




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    495

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49657

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    497
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    498

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49662
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49664
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49666

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49670

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149675

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149677

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49680

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49683

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49686

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____149688

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49695

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49702

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49704
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49705

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49706
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49707
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49708
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49709

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49715

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49704
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49705

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49706
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49707
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49708
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49722

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49704
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49730
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49731

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49736

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49739
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49741

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49744

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149748

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149752

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4989

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    Java




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49759

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49760
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49761

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49760
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49763

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    251

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49772
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49666

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49778
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    308
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49780
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149675

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149677

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49789
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49791

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49794
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49686

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49801
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49695

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49702

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49818
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49821

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49715

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49831

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49730
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49850

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49818
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49854
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288_______1289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49861
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49863
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    296

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49818

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49818
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49867

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49818
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49869

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49872
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49872
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49863
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49872
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49892

    Python3




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49894

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49896
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    308

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    000
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    223
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    003
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    007

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    009

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    000
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    014
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    020
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    022
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    028

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49896
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322____190

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    000
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    044
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    047

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    051
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    052

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    370
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    055____2341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    047

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    051
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    063

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49730
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

     

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    073____2341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    076
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    079
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49861
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49863
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    213

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    093
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    097

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    093
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49863

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    097

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    093
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    097

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    110

    C#




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    249

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    115

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49766
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    123
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49666

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    129

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    132

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149675

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149677

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49680

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____149683

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49686

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____149688

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49695

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49702

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    167

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49715

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    177

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    183
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49730
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    194

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    197

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49744

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149748

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149752

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49892

    Javascript




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49595

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49460
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    217

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    220

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    222

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    224

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149675

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____149677

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49680

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49686

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____149688

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49695

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49702

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    255
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    167

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49715

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    255
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49820
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    267

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    255
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49730
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    280

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    281

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49748

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49746

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49752

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49746

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    287

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49655

    Đầu ra

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3

    Độ phức tạp về thời gian. O (log n)
    Không gian phụ. Ô (1)

    Triển khai lặp lại Tìm kiếm nhị phân 
     

    C++




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    495

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    497
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    498

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    294

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    310

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    313

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    315

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    321

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____1323

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    328

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    330

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    338

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    340

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4958____14959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4964

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4970
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4972
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4974

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4977

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4979

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4981
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4984
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4985
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4986

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4989

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    C




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    379

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    02

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    294

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    8
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    20
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    310

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    313

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    315

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    321

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____1323

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    328

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    330

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    338

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    340

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4958____14959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4964

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4970
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4972
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4971
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4974

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4977

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    454
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    85
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    457

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49546
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    459____14960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49651
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    85
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    465

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49546
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    467
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49546____1470

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4989

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    Java




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    475

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    201

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    479

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    481

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    6
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    493
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    308
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    495
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    310

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    503
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    315

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    321

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    323

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    520____1247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    330

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____2322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    528
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    338

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    340

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266____1247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    272

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    277

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    281______1282
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    283

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    286
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    296

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    299

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    302____1293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    580

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    314
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    319
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    594

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    597
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    327

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

    Python3




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    602

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    603

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    604

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    605

     

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    335

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    610
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    612

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    346
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    348
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    350
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    351
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    625

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    358
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    361

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    636

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    370
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    639

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    346
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    647

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322____190

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    652
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    344
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    658

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    660

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266____1247

     

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    201
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    225
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    289
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    291
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    295
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    213

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    214
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    293

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    217

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    218
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    220
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    308
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    223
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    224
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    377

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    229____2341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    247
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    237
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    238
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    239

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    90

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    235____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

    C#




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    712

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    496
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    249

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    200
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    251

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    479

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    481

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    261
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    22

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    733

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    310

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    313

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    315

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    318

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    321

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    323

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    326

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    328

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    330

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37____2322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    234
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    334

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    338

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    340

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    272

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    274
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    275
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4959
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49420

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

    _______127____13____149425

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49428

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    3
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    792

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4979

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    319
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49439
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    594

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49447
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    347
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    597
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    327

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    812

    PHP




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49453

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49454

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    815

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    816

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49457

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49458

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    819

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49460
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4____149462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    826
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    288
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    836
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49484
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    266
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    849

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    315

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49499
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49504____186
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    868

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    870

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    203
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    877
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49464
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    884

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    886

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    888

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49466
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    842
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    895

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    899

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    901

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49557

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341____149560
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49561

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49562
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    341
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49564
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    86
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49569

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49570
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49571____149462
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49573

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    923
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49562
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49532
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49468
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    320

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49579
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49570
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49581

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49582
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    226

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49582
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4985____1288

    _______149546____149570____1226

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49593

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49594

    Javascript




        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49595

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    945

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    294

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    1

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    946
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49460
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    952

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    953

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____1955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    957

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    224

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49679
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    963
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    964

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    31

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    33

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    36

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    39

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    21

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    23

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    25
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    26

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    985

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14941

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27____14943

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    27
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    322

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    37
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    994

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    946

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4950

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____14952

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    38
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4955

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4948

     

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2007
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    282
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2009

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24____14967

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    299

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    792

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    24

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49648
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4982
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    4960

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2020
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2021____14985
        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    327

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2020

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2025

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    49655

    Đầu ra

        binarySearch(arr, x, low, high)
               if low > high
                   return False 
       
               else
                   mid = (low + high) / 2 
                       if x == arr[mid]
                       return mid
           
                   else if x > arr[mid]        // x is on the right side
                       return binarySearch(arr, x, mid + 1, high)
                   
                   else                        // x is on the left side
                       return binarySearch(arr, x, low, mid - 1) 
    2

    Độ phức tạp về thời gian. O(log n)
    Không gian phụ. Ô(1)

    Mô hình thuật toán. Giảm và chinh phục

    Ghi chú. Ở đây chúng tôi đang sử dụng

    int mid = thấp + (cao – thấp)/2;

    Có thể, bạn thắc mắc tại sao chúng ta lại tính chỉ số trung bình theo cách này, chúng ta chỉ cần cộng chỉ số thấp hơn và chỉ số cao hơn rồi chia cho 2

    int mid = (thấp + cao)/2;

    Nhưng nếu chúng ta tính chỉ số giữa như thế này có nghĩa là code của chúng ta không đúng 100%, nó có lỗi

    Đó là, nó không thành công đối với các giá trị lớn hơn của biến int thấp và cao. Cụ thể, nó không thành công nếu tổng giá trị thấp và cao lớn hơn giá trị int dương tối đa(231 – 1 )

    Tổng tràn thành giá trị âm và giá trị này vẫn âm khi chia cho 2.
    Trong java, nó ném ngoại lệ ArrayIndexOutOfBoundException.

    int mid = thấp + (cao – thấp)/2;

    Vì vậy, tốt hơn là sử dụng nó như thế này. Lỗi này áp dụng như nhau cho sắp xếp hợp nhất và các thuật toán phân chia và chinh phục khác