Maximum Subarray Sum Using Divide and Conquer Algorithm in C++

Suppose we have one list of data with positive and negative values. We have to find the sum of contiguous subarray whose sum is largest. Suppose the list is containing {-2, -5, 6, -2, -3, 1, 5, -6}, then the sum of maximum subarray is 7. It is the sum of {6, -2, -3, 1, 5}

We will solve this problem by using the Divide and Conquer method. The steps will look like below −

Steps −

• Divide the array into two parts
• Find the maximum of the following three
  • Maximum subarray sum of left subarray
  • Maximum subarray sum of right subarray
  • Maximum subarray sum such that subarray crosses the midpoint

Example

#include <iostream> using namespace std; int max(int a, int b) {    return (a > b)? a : b; } int max(int a, int b, int c) {    return max(max(a, b), c); } int getMaxCrossingSum(int arr[], int l, int m, int h) {    int sum = 0;    int left = INT_MIN;    for (int i = m; i >= l; i--) {       sum = sum + arr[i];       if (sum > left)       left = sum;    }    sum = 0;    int right = INT_MIN;    for (int i = m+1; i <= h; i++) {       sum = sum + arr[i];       if (sum > right)       right = sum;    }    return left + right; } int maxSubArraySum(int arr[], int low, int high) {    if (low == high)    return arr[low];    int mid = (low + high)/2;    return max(maxSubArraySum(arr, low, mid), maxSubArraySum(arr, mid+1, high), getMaxCrossingSum(arr, low, mid, high)); } int main() {    int arr[] = {-2, -5, 6, -2, -3, 1, 5, -6};    int n = sizeof(arr)/sizeof(arr[0]);    int max_sum = maxSubArraySum(arr, 0, n-1);    printf("Maximum contiguous sum is %d", max_sum); }

Output

Valid String