# C++ Programming – Largest Sum Contiguous Subarray

C++ Programming - Largest Sum Contiguous Subarray - Dynamic Programming Write a program to find the sum of contiguous subarray within one-dimensional array

Write an efficient C++ program to find the sum of contiguous subarray within a one-dimensional array of numbers which has the largest sum. Kadane’s Algorithm:

```Initialize:
max_so_far = 0
max_ending_here = 0

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

Explanation:
Simple idea of the 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 =  -2
max_ending_here = max_ending_here + (-2)
Set max_ending_here = 0 because max_ending_here < 0

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

for i=2,  a =  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 =  -1
max_ending_here = max_ending_here + (-1)
max_ending_here = 3

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

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

for i=6,  a =  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 =  -3
max_ending_here = max_ending_here + (-3)
max_ending_here = 4
```

Program:

C++
``````// C++ program to print largest contiguous array sum
#include<iostream>
#include<climits>
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);
int max_sum = maxSubArraySum(a, n);
cout << "Maximum contiguous sum is " << max_sum;
return 0;
}``````

Output :

`Maximum contiguous sum is 7`

Above program can be optimized further, if we compare max_so_far with max_ending_here only if max_ending_here is greater than 0.

C++
``````int maxSubArraySum(int a[], int size)
{
int max_so_far = 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;
}``````

Time Complexity: O(n)
Algorithmic Paradigm: Dynamic Programming

READ  C Program Print BST keys in the given range

The implementation handles the case when all numbers in array are negative.

C++
``````#include<iostream>
using namespace std;

int maxSubArraySum(int a[], int size)
{
int max_so_far = a;
int curr_max = a;

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);
int max_sum = maxSubArraySum(a, n);
cout << "Maximum contiguous sum is " << max_sum;
return 0;
}``````

Output :

`Maximum contiguous sum is 7`

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<iostream>
#include<climits>
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);
int max_sum = maxSubArraySum(a, n);
return 0;
}``````

Output :

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

#### About the author #### Venkatesan Prabu

Wikitechy Founder, Author, International Speaker, and Job Consultant. My role as the CEO of Wikitechy, I help businesses build their next generation digital platforms and help with their product innovation and growth strategy. I'm a frequent speaker at tech conferences and events.

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