Hướng dẫn how to find contiguous subarrays in python - cách tìm các mảng con liền kề trong python

Question

Giải pháp một dòng (Tôi không biết điều gì có nghĩa là "cách tốt hơn" cho bạn)

Nội dung chính Show

Làm thế nào để tôi tìm thấy Subarrays trong Python?
Subarrays tiếp giáp là gì?
Subarray tiếp giáp trong Python là gì?

L = [1,2,3]
[L[i:i+j] for i in range(0,len(L)) for j in range(1,len(L)-i+1)]

L=[1,2,3,4]
[L[i:i+j] for i in range(0,len(L)) for j in range(1,len(L)-i+1)]

bạn lấy,

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

Viết một chương trình hiệu quả để tìm tổng số subarray liên tục trong một mảng một chiều các số có số tiền lớn nhất. & NBSP;

Hướng dẫn how to find contiguous subarrays in python - cách tìm các mảng con liền kề trong python

Thuật toán Kadane từ:

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

Giải thích: & nbsp; Ý tưởng đơn giản của thuật toán Kadane, là tìm kiếm tất cả các phân đoạn tiếp giáp tích cực của mảng (MAX_IVED_HERE được sử dụng cho việc này). Và theo dõi phân đoạn liên tục tổng tối đa trong số tất cả các phân đoạn dương (MAX_SO_FAR được sử dụng cho việc này). Mỗi lần chúng tôi nhận được một tổng dương so sánh nó với MAX_SO_FAR và cập nhật MAX_SO_FAR nếu nó lớn hơn MAX_SO_FAR & NBSP;
The simple idea of Kadane’s algorithm is to look for all positive contiguous segments of the array (max_ending_here is used for this). And keep track of maximum sum contiguous segment among all positive segments (max_so_far is used for this). Each time we get a positive-sum compare it with max_so_far and update max_so_far if it is greater than max_so_far

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

Program:

Python3

from math import

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

1

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

8

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

9

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

1

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

9

Maximum contiguous sum is 7

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

3

Maximum contiguous sum is 7

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7

7

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

0

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

4

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2 ________ 26 & nbsp; & nbsp;

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Maximum contiguous sum is 7

8

Maximum contiguous sum is 7

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from0

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from3

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 5

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 8

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import1

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

00

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

Is

Output:

Maximum contiguous sum is 7

Cách tiếp cận khác:

Python3

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

8

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

9

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

1

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

9

Maximum contiguous sum is 7

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

0

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

4

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2 ________ 26 & nbsp; & nbsp;

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Maximum contiguous sum is 7

8

Maximum contiguous sum is 7

9

Maximum contiguous sum is 7

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Maximum contiguous sum is 7

8

Maximum contiguous sum is 7

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

0
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
2
Maximum contiguous sum is 7 Starting index 2 Ending index 6
2
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9
Maximum contiguous sum is 7 Starting index 2 Ending index 6
4
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9
Maximum contiguous sum is 7 Starting index 2 Ending index 6
7
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9from0
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9from3
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9
Maximum contiguous sum is 7 Starting index 2 Ending index 6
7
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9from9
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9math 2
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9math 5
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9math 8
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9import1
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9import4
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9import7
Maximum contiguous sum is 7 Starting index 2 Ending index 6
5
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
9
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
00
[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]] [[1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [2], [2, 3], [2, 3, 4], [3], [3, 4], [4]]
01O(n)

IsDynamic Programming
Following is another simple implementation suggested by Mohit Kumar. The implementation handles the case when all numbers in the array are negative.

Python3

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

13

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

8

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

9

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

1

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

9

Maximum contiguous sum is 7

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Maximum contiguous sum is 7

8

Maximum contiguous sum is 7

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from0

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from3

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 5

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 8

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import1

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

00

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

Is

Output:

Maximum contiguous sum is 7

Cách tiếp cận khác:

Python3

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

13

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

8

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

9

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

1

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

9

Maximum contiguous sum is 7

0

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

3

Maximum contiguous sum is 7

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7

7

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

0

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

4

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2 ________ 26 & nbsp; & nbsp;

Maximum contiguous sum is 7

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

7

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7

7

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

0

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

4

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2 ________ 26 & nbsp; & nbsp;

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

5

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

0

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

6

Maximum contiguous sum is 7

2

Maximum contiguous sum is 7

4

Initialize:
    max_so_far = INT_MIN
    max_ending_here = 0

Loop for each element of the array
  (a) max_ending_here = max_ending_here + a[i]
  (b) if(max_so_far < max_ending_here)
            max_so_far = max_ending_here
  (c) if(max_ending_here < 0)
            max_ending_here = 0
return max_so_far

4

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2 ________ 26 & nbsp; & nbsp;

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

6

Maximum contiguous sum is 7

8

Maximum contiguous sum is 7

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from0

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from3

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 5

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 8

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import1

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

00

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

Is

Cách tiếp cận khác:

Maximum contiguous sum is 7
Starting index 2
Ending index 6

0

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

2

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from0

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from3

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9from9

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 2

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 5

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9math 8

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import1

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import4

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9import7

Maximum contiguous sum is 7
Starting index 2
Ending index 6

5

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

9

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

00

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

01

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

34

[[1], [1, 2], [1, 2, 3], [2], [2, 3], [3]]

[[1],
 [1, 2],
 [1, 2, 3],
 [1, 2, 3, 4],
 [2],
 [2, 3],
 [2, 3, 4],
 [3],
 [3, 4],
 [4]]

06

    Lets take the example:
    {-2, -3, 4, -1, -2, 1, 5, -3}

    max_so_far = max_ending_here = 0

    for i=0,  a[0] =  -2
    max_ending_here = max_ending_here + (-2)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=1,  a[1] =  -3
    max_ending_here = max_ending_here + (-3)
    Set max_ending_here = 0 because max_ending_here < 0

    for i=2,  a[2] =  4
    max_ending_here = max_ending_here + (4)
    max_ending_here = 4
    max_so_far is updated to 4 because max_ending_here greater 
    than max_so_far which was 0 till now

    for i=3,  a[3] =  -1
    max_ending_here = max_ending_here + (-1)
    max_ending_here = 3

    for i=4,  a[4] =  -2
    max_ending_here = max_ending_here + (-2)
    max_ending_here = 1

    for i=5,  a[5] =  1
    max_ending_here = max_ending_here + (1)
    max_ending_here = 2

    for i=6,  a[6] =  5
    max_ending_here = max_ending_here + (5)
    max_ending_here = 7
    max_so_far is updated to 7 because max_ending_here is 
    greater than max_so_far

    for i=7,  a[7] =  -3
    max_ending_here = max_ending_here + (-3)
    max_ending_here = 4

36

Output:

Maximum contiguous sum is 7
Starting index 2
Ending index 6

Is

Độ phức tạp về thời gian: O (n)O(n)

Không gian phụ trợ: O (1)O(1)

Bây giờ hãy thử câu hỏi dưới đây & nbsp; đưa ra một loạt các số nguyên (có thể là một số yếu tố âm), hãy viết một chương trình C để tìm ra * sản phẩm tối đa * có thể bằng cách nhân các số nguyên liên tiếp trong mảng trong đó n ≤ mảng_size. Ngoài ra, in điểm bắt đầu của sản phẩm tối đa Subarray.
Given an array of integers (possibly some elements negative), write a C program to find out the *maximum product* possible by multiplying ‘n’ consecutive integers in the array where n ≤ ARRAY_SIZE. Also, print the starting point of the maximum product subarray.

Vui lòng viết nhận xét nếu bạn tìm thấy bất cứ điều gì không chính xác, hoặc bạn muốn chia sẻ thêm thông tin về chủ đề được thảo luận ở trên.

Làm thế nào để tôi tìm thấy Subarrays trong Python?

Để có được Subarray, chúng ta có thể sử dụng cắt lát để lấy Subarray.Bước 1: Chạy vòng lặp cho đến chiều dài+1 của danh sách đã cho.Bước 2: Chạy một vòng lặp khác từ 0 đến i.Bước 3: Cắt lát Subarray từ J đến i.use slicing to get the subarray. Step 1: Run a loop till length+1 of the given list. Step 2: Run another loop from 0 to i. Step 3: Slice the subarray from j to i.

Subarrays tiếp giáp là gì?

Một subarray liền kề chỉ đơn giản là một subarray của một mảng có điều kiện là các phần tử của subarray phải theo trình tự chính xác như là chuỗi của các phần tử trong mảng.a subarray of an array with a condition that the elements of the subarray should be in exact sequence as the sequence of the elements in the array.

Subarray tiếp giáp trong Python là gì?

Cho một mảng số, trả về true nếu có một SubArray tổng hợp lên đến một số n nhất định.Một Subarray là một tập hợp con tiếp giáp của mảng.Ví dụ, subarray của [1,2,3,4,5] là [1,2,3] hoặc [3,4,5] hoặc [2,3,4], v.v.a contiguous subset of the array. For example the subarray of [1,2,3,4,5] is [1,2,3] or [3,4,5] or [2,3,4] etc.

programming python Contiguous subarrays Python Select subarray Python

Hướng dẫn how to find contiguous subarrays in python - cách tìm các mảng con liền kề trong python

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Làm thế nào để tôi tìm thấy Subarrays trong Python?

Subarrays tiếp giáp là gì?

Subarray tiếp giáp trong Python là gì?

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