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

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.  

Ví dụ về thuật toán tìm kiếm nhị phân

Đề nghị thực hành

Tìm kiếm nhị phân

Thử nó

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

Chủ Đề