# Largest Sum Contiguous Subarray

• Difficulty Level : Medium
• Last Updated : 24 Jun, 2022

Write an efficient program to find the sum of the contiguous subarray within a one-dimensional array of numbers that has the largest sum.

```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```

Explanation:
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 the 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 = INT_MIN
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
and set max_so_far = -2

for i=1,  a[1] =  -3
max_ending_here = max_ending_here + (-3)
Since max_ending_here = -3 and max_so_far = -2, max_so_far will remain -2
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 -2 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```

Note: The above algorithm only works if and only if at least one positive number should be present otherwise it does not work i.e if an Array contains all negative numbers it doesn’t work.

Program:

## C++

 `// C++ program to print largest contiguous array sum` `#include` `#include` `using` `namespace` `std;`   `int` `maxSubArraySum(``int` `a[], ``int` `size)` `{` `    ``int` `max_so_far = INT_MIN, max_ending_here = 0;`   `    ``for` `(``int` `i = 0; i < size; i++)` `    ``{` `        ``max_ending_here = max_ending_here + a[i];` `        ``if` `(max_so_far < max_ending_here)` `            ``max_so_far = max_ending_here;`   `        ``if` `(max_ending_here < 0)` `            ``max_ending_here = 0;` `    ``}` `    ``return` `max_so_far;` `}`   `/*Driver program to test maxSubArraySum*/` `int` `main()` `{` `    ``int` `a[] = {-2, -3, 4, -1, -2, 1, 5, -3};` `    ``int` `n = ``sizeof``(a)/``sizeof``(a[0]);` `    ``int` `max_sum = maxSubArraySum(a, n);` `    ``cout << ``"Maximum contiguous sum is "` `<< max_sum;` `    ``return` `0;` `}`

## Java

 `import` `java.io.*;` `// Java program to print largest contiguous array sum` `import` `java.util.*;`   `class` `Kadane` `{` `    ``public` `static` `void` `main (String[] args)` `    ``{` `        ``int` `[] a = {-``2``, -``3``, ``4``, -``1``, -``2``, ``1``, ``5``, -``3``};` `        ``System.out.println(``"Maximum contiguous sum is "` `+` `                                       ``maxSubArraySum(a));` `    ``}`   `    ``static` `int` `maxSubArraySum(``int` `a[])` `    ``{` `        ``int` `size = a.length;` `        ``int` `max_so_far = Integer.MIN_VALUE, max_ending_here = ``0``;`   `        ``for` `(``int` `i = ``0``; i < size; i++)` `        ``{` `            ``max_ending_here = max_ending_here + a[i];` `            ``if` `(max_so_far < max_ending_here)` `                ``max_so_far = max_ending_here;` `            ``if` `(max_ending_here < ``0``)` `                ``max_ending_here = ``0``;` `        ``}` `        ``return` `max_so_far;` `    ``}` `}`

## Python

 `# Python program to find maximum contiguous subarray` ` `  `# Function to find the maximum contiguous subarray` `from` `sys ``import` `maxint` `def` `maxSubArraySum(a,size):` `     `  `    ``max_so_far ``=` `-``maxint ``-` `1` `    ``max_ending_here ``=` `0` `     `  `    ``for` `i ``in` `range``(``0``, size):` `        ``max_ending_here ``=` `max_ending_here ``+` `a[i]` `        ``if` `(max_so_far < max_ending_here):` `            ``max_so_far ``=` `max_ending_here`   `        ``if` `max_ending_here < ``0``:` `            ``max_ending_here ``=` `0`   `    ``return` `max_so_far` ` `  `# Driver function to check the above function `   `a ``=` `[``-``2``, ``-``3``, ``4``, ``-``1``, ``-``2``, ``1``, ``5``, ``-``3``]`   `print` `"Maximum contiguous sum is"``, maxSubArraySum(a,``len``(a))` ` `  `#This code is contributed by _Devesh Agrawal_`

## C#

 `// C# program to print largest ` `// contiguous array sum` `using` `System;`   `class` `GFG` `{` `    ``static` `int` `maxSubArraySum(``int` `[]a)` `    ``{` `        ``int` `size = a.Length;` `        ``int` `max_so_far = ``int``.MinValue, ` `            ``max_ending_here = 0;`   `        ``for` `(``int` `i = 0; i < size; i++)` `        ``{` `            ``max_ending_here = max_ending_here + a[i];` `            `  `            ``if` `(max_so_far < max_ending_here)` `                ``max_so_far = max_ending_here;` `            `  `            ``if` `(max_ending_here < 0)` `                ``max_ending_here = 0;` `        ``}` `        `  `        ``return` `max_so_far;` `    ``}` `    `  `    ``// Driver code ` `    ``public` `static` `void` `Main ()` `    ``{` `        ``int` `[] a = {-2, -3, 4, -1, -2, 1, 5, -3};` `        ``Console.Write(``"Maximum contiguous sum is "` `+` `                                ``maxSubArraySum(a));` `    ``}`   `}`   `// This code is contributed by Sam007_`

## PHP

 ``

## Javascript

 ``

Output

`Maximum contiguous sum is 7`

Time Complexity: O(n)
Auxiliary Space: O(1)

Another approach:

## C++

 `int` `maxSubarraySum(``int` `arr[], ``int` `size)` `{` `    ``int` `max_ending_here = 0, max_so_far = INT_MIN;` `    ``for` `(``int` `i = 0; i < size; i++) {` `      `  `        ``// include current element to previous subarray only` `        ``// when it can add to a bigger number than itself.` `        ``if` `(arr[i] <= max_ending_here + arr[i]) {` `            ``max_ending_here += arr[i];` `        ``}` `      `  `        ``// Else start the max subarray from current element` `        ``else` `{` `            ``max_ending_here = arr[i];` `        ``}` `        ``if` `(max_ending_here > max_so_far)` `            ``max_so_far = max_ending_here;` `    ``}` `    ``return` `max_so_far;` `} ``// contributed by Vipul Raj`

## Java

 `static` `int` `maxSubArraySum(``int` `a[],``int` `size) ` `{ ` `    `  `    ``int` `max_so_far = a[``0``], max_ending_here = ``0``; `   `    ``for` `(``int` `i = ``0``; i < size; i++) ` `    ``{ ` `        ``max_ending_here = max_ending_here + a[i];` `        ``if` `(max_ending_here < ``0``) ` `            ``max_ending_here = ``0``; ` `        `  `        ``/* Do not compare for all` `           ``elements. Compare only ` `           ``when max_ending_here > 0 */` `        ``else` `if` `(max_so_far < max_ending_here) ` `            ``max_so_far = max_ending_here; ` `        `  `    ``} ` `    ``return` `max_so_far; ` `} `   `// This code is contributed by ANKITRAI1`

## Python

 `def` `maxSubArraySum(a,size):` `    `  `    ``max_so_far ``=` `a[``0``]` `    ``max_ending_here ``=` `0` `    `  `    ``for` `i ``in` `range``(``0``, size):` `        ``max_ending_here ``=` `max_ending_here ``+` `a[i]` `        ``if` `max_ending_here < ``0``:` `            ``max_ending_here ``=` `0` `        `  `        ``# Do not compare for all elements. Compare only   ` `        ``# when  max_ending_here > 0` `        ``elif` `(max_so_far < max_ending_here):` `            ``max_so_far ``=` `max_ending_here` `            `  `    ``return` `max_so_far`

## C#

 `static` `int` `maxSubArraySum(``int``[] a, ``int` `size)` `{` `    ``int` `max_so_far = a[0], max_ending_here = 0;`   `    ``for` `(``int` `i = 0; i < size; i++) {` `        ``max_ending_here = max_ending_here + a[i];` `        ``if` `(max_ending_here < 0)` `            ``max_ending_here = 0;`   `        ``/* Do not compare for all` `        ``elements. Compare only` `        ``when max_ending_here > 0 */` `        ``else` `if` `(max_so_far < max_ending_here)` `            ``max_so_far = max_ending_here;` `    ``}` `    ``return` `max_so_far;` `}`   `// This code is contributed` `// by ChitraNayal`

## PHP

 ` 0 */` `    ``else` `if` `(``\$max_so_far` `< ``\$max_ending_here``)` `        ``\$max_so_far` `= ``\$max_ending_here``;` `}` `return` `\$max_so_far``;`   `// This code is contributed` `// by ChitraNayal` `?>`

## Javascript

 ``

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

## C++

 `#include` `using` `namespace` `std;`   `int` `maxSubArraySum(``int` `a[], ``int` `size)` `{` `   ``int` `max_so_far = a[0];` `   ``int` `curr_max = a[0];`   `   ``for` `(``int` `i = 1; i < size; i++)` `   ``{` `        ``curr_max = max(a[i], curr_max+a[i]);` `        ``max_so_far = max(max_so_far, curr_max);` `   ``}` `   ``return` `max_so_far;` `}`   `/* Driver program to test maxSubArraySum */` `int` `main()` `{` `   ``int` `a[] =  {-2, -3, 4, -1, -2, 1, 5, -3};` `   ``int` `n = ``sizeof``(a)/``sizeof``(a[0]);` `   ``int` `max_sum = maxSubArraySum(a, n);` `   ``cout << ``"Maximum contiguous sum is "` `<< max_sum;` `   ``return` `0;` `}`

## Java

 `// Java program to print largest contiguous` `// array sum` `import` `java.io.*;`   `class` `GFG {`   `    ``static` `int` `maxSubArraySum(``int` `a[], ``int` `size)` `    ``{` `    ``int` `max_so_far = a[``0``];` `    ``int` `curr_max = a[``0``];`   `    ``for` `(``int` `i = ``1``; i < size; i++)` `    ``{` `           ``curr_max = Math.max(a[i], curr_max+a[i]);` `        ``max_so_far = Math.max(max_so_far, curr_max);` `    ``}` `    ``return` `max_so_far;` `    ``}`   `    ``/* Driver program to test maxSubArraySum */` `    ``public` `static` `void` `main(String[] args)` `    ``{` `    ``int` `a[] = {-``2``, -``3``, ``4``, -``1``, -``2``, ``1``, ``5``, -``3``};` `    ``int` `n = a.length;   ` `    ``int` `max_sum = maxSubArraySum(a, n);` `    ``System.out.println(``"Maximum contiguous sum is "` `                       ``+ max_sum);` `    ``}` `}`   `// This code is contributed by Prerna Saini`

## Python

 `# Python program to find maximum contiguous subarray`   `def` `maxSubArraySum(a,size):` `    `  `    ``max_so_far ``=``a[``0``]` `    ``curr_max ``=` `a[``0``]` `    `  `    ``for` `i ``in` `range``(``1``,size):` `        ``curr_max ``=` `max``(a[i], curr_max ``+` `a[i])` `        ``max_so_far ``=` `max``(max_so_far,curr_max)` `        `  `    ``return` `max_so_far`   `# Driver function to check the above function ` `a ``=` `[``-``2``, ``-``3``, ``4``, ``-``1``, ``-``2``, ``1``, ``5``, ``-``3``]` `print``"Maximum contiguous sum is"` `, maxSubArraySum(a,``len``(a))`   `#This code is contributed by _Devesh Agrawal_`

## C#

 `// C# program to print largest ` `// contiguous array sum` `using` `System;`   `class` `GFG` `{` `    ``static` `int` `maxSubArraySum(``int` `[]a, ``int` `size)` `    ``{` `    ``int` `max_so_far = a[0];` `    ``int` `curr_max = a[0];`   `    ``for` `(``int` `i = 1; i < size; i++)` `    ``{` `        ``curr_max = Math.Max(a[i], curr_max+a[i]);` `        ``max_so_far = Math.Max(max_so_far, curr_max);` `    ``}`   `    ``return` `max_so_far;` `    ``}`   `    ``// Driver code ` `    ``public` `static` `void` `Main ()` `    ``{` `        ``int` `[]a = {-2, -3, 4, -1, -2, 1, 5, -3};` `        ``int` `n = a.Length; ` `        ``Console.Write(``"Maximum contiguous sum is "` `                           ``+ maxSubArraySum(a, n));` `    ``}`   `}`   `// This code is contributed by Sam007_`

## PHP

 ``

## Javascript

 ``

Output

`Maximum contiguous sum is 7`

Time complexity: O(n), where n is the size of the array.
Auxiliary Space: O(1)

To print the subarray with the maximum sum, we maintain indices whenever we get the maximum sum.

## C++

 `// C++ program to print largest contiguous array sum` `#include` `#include` `using` `namespace` `std;`   `int` `maxSubArraySum(``int` `a[], ``int` `size)` `{` `    ``int` `max_so_far = INT_MIN, max_ending_here = 0,` `       ``start =0, end = 0, s=0;`   `    ``for` `(``int` `i=0; i< size; i++ )` `    ``{` `        ``max_ending_here += a[i];`   `        ``if` `(max_so_far < max_ending_here)` `        ``{` `            ``max_so_far = max_ending_here;` `            ``start = s;` `            ``end = i;` `        ``}`   `        ``if` `(max_ending_here < 0)` `        ``{` `            ``max_ending_here = 0;` `            ``s = i + 1;` `        ``}` `    ``}` `    ``cout << ``"Maximum contiguous sum is "` `        ``<< max_so_far << endl;` `    ``cout << ``"Starting index "``<< start` `        ``<< endl << ``"Ending index "``<< end << endl;` `}`   `/*Driver program to test maxSubArraySum*/` `int` `main()` `{` `    ``int` `a[] = {-2, -3, 4, -1, -2, 1, 5, -3};` `    ``int` `n = ``sizeof``(a)/``sizeof``(a[0]);` `    ``int` `max_sum = maxSubArraySum(a, n);` `    ``return` `0;` `}`

## Java

 `// Java program to print largest ` `// contiguous array sum` `class` `GFG {`   `    ``static` `void` `maxSubArraySum(``int` `a[], ``int` `size)` `    ``{` `        ``int` `max_so_far = Integer.MIN_VALUE,` `        ``max_ending_here = ``0``,start = ``0``,` `        ``end = ``0``, s = ``0``;`   `        ``for` `(``int` `i = ``0``; i < size; i++) ` `        ``{` `            ``max_ending_here += a[i];`   `            ``if` `(max_so_far < max_ending_here) ` `            ``{` `                ``max_so_far = max_ending_here;` `                ``start = s;` `                ``end = i;` `            ``}`   `            ``if` `(max_ending_here < ``0``) ` `            ``{` `                ``max_ending_here = ``0``;` `                ``s = i + ``1``;` `            ``}` `        ``}` `        ``System.out.println(``"Maximum contiguous sum is "` `                           ``+ max_so_far);` `        ``System.out.println(``"Starting index "` `+ start);` `        ``System.out.println(``"Ending index "` `+ end);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `a[] = { -``2``, -``3``, ``4``, -``1``, -``2``, ``1``, ``5``, -``3` `};` `        ``int` `n = a.length;` `        ``maxSubArraySum(a, n);` `    ``}` `}`   `// This code is contributed by  prerna saini`

## Python3

 `# Python program to print largest contiguous array sum`   `from` `sys ``import` `maxsize`   `# Function to find the maximum contiguous subarray` `# and print its starting and end index` `def` `maxSubArraySum(a,size):`   `    ``max_so_far ``=` `-``maxsize ``-` `1` `    ``max_ending_here ``=` `0` `    ``start ``=` `0` `    ``end ``=` `0` `    ``s ``=` `0`   `    ``for` `i ``in` `range``(``0``,size):`   `        ``max_ending_here ``+``=` `a[i]`   `        ``if` `max_so_far < max_ending_here:` `            ``max_so_far ``=` `max_ending_here` `            ``start ``=` `s` `            ``end ``=` `i`   `        ``if` `max_ending_here < ``0``:` `            ``max_ending_here ``=` `0` `            ``s ``=` `i``+``1`   `    ``print` `(``"Maximum contiguous sum is %d"``%``(max_so_far))` `    ``print` `(``"Starting Index %d"``%``(start))` `    ``print` `(``"Ending Index %d"``%``(end))`   `# Driver program to test maxSubArraySum` `a ``=` `[``-``2``, ``-``3``, ``4``, ``-``1``, ``-``2``, ``1``, ``5``, ``-``3``]` `maxSubArraySum(a,``len``(a))`

## C#

 `// C# program to print largest ` `// contiguous array sum` `using` `System;`   `class` `GFG ` `{` `    ``static` `void` `maxSubArraySum(``int` `[]a, ` `                               ``int` `size)` `    ``{` `        ``int` `max_so_far = ``int``.MinValue,` `        ``max_ending_here = 0, start = 0,` `        ``end = 0, s = 0;`   `        ``for` `(``int` `i = 0; i < size; i++) ` `        ``{` `            ``max_ending_here += a[i];`   `            ``if` `(max_so_far < max_ending_here) ` `            ``{` `                ``max_so_far = max_ending_here;` `                ``start = s;` `                ``end = i;` `            ``}`   `            ``if` `(max_ending_here < 0) ` `            ``{` `                ``max_ending_here = 0;` `                ``s = i + 1;` `            ``}` `        ``}` `        ``Console.WriteLine(``"Maximum contiguous "` `+ ` `                         ``"sum is "` `+ max_so_far);` `        ``Console.WriteLine(``"Starting index "` `+ ` `                                      ``start);` `        ``Console.WriteLine(``"Ending index "` `+ ` `                                      ``end);` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `Main()` `    ``{` `        ``int` `[]a = {-2, -3, 4, -1, ` `                   ``-2, 1, 5, -3};` `        ``int` `n = a.Length;` `        ``maxSubArraySum(a, n);` `    ``}` `}`   `// This code is contributed` `// by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output

```Maximum contiguous sum is 7
Starting index 2
Ending index 6
```

Kadane’s Algorithm can be viewed both as greedy and DP. As we can see that we are keeping a running sum of integers and when it becomes less than 0, we reset it to 0 (Greedy Part). This is because continuing with a negative sum is way worse than restarting with a new range. Now it can also be viewed as a DP, at each stage we have 2 choices: Either take the current element and continue with the previous sum OR restart a new range. Both choices are being taken care of in the implementation.
Time Complexity: O(n)
Auxiliary Space: O(1)

Now try the below question
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.