Size of sub-array with max sum in C

March 28, 2023

Size of sub-array with max sum

Here, in this page we will discuss the program to find size of sub-array with max sum in C. We use Kadane’s algorithm, which runs in O(n) time.
The idea is to keep scanning through the array and calculating the maximum sub-array that ends at every position. If current sum becomes 0 then at that point we also update the starting index.

Size of sub-array with max sum in C

The size of the sub-array with the maximum sum in an array is the number of elements that are part of that sub-array.

For example, in the array

[1, -2, 3, 5, -3, 2], the sub-array with the maximum sum is [3, 5], and its size is 2.

To find the size of the sub-array with the maximum sum in C, you can modify the Kadane’s algorithm implementation to keep track of the size of the sub-array as well.

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Algorithm:

Create two intermediate variables max_ending_here and max_so_far .
And also two variables start and end for tracking start and the end index of the subarray with maximum sum.
Initialized these two intermediate variables using the 0.
Traverse the array from 0 to N-1 and calculate the max_ending_here and max_so_far.
Now we will keep max_so_far which indicates the maximum sum found so far.
During the scanning of the elements from starting, and when the max_ending_here becomes 0 at that point we also update start and end variables.

Note The time complexity of above algorithm to find the maximum subarray sum and its size is O(n)

C code for Size of sub-array with max sum

Run

#include<stdio.h>

int maxSubArraySum(int a[], int size)
{
    int max_so_far = 0, 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;
        }
    }
     
    return (end - start + 1);
}
 
int main()
{
    int a[] = {-7, 3, 4, -1, -12, 1, -9, -3};
    int n = sizeof(a)/sizeof(a[0]);
    printf("Size of subarray with maximum sum is : %d",maxSubArraySum(a, n));
    return 0;
}

Output

Size of subarray with maximum sum is : 2

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