find maximum sum in array of contiguous subarrays

To find the maximum sum in an array of contiguous subarrays in C++, you can use the Kadane's algorithm. Here are the steps:

1. Initialize two variables, max_so_far and max_ending_here, to track the maximum sum. Set both variables to 0 initially.

2. Iterate through the array, element by element.

3. For each element, add it to the max_ending_here variable.

4. If the max_ending_here variable becomes negative, reset it to 0. This is because a negative sum will only decrease the overall maximum sum.

5. If the max_ending_here variable is greater than the max_so_far variable, update the max_so_far variable with the max_ending_here value.

6. After iterating through the entire array, the max_so_far variable will contain the maximum sum of any contiguous subarray in the array.

Here is an example implementation of the Kadane's algorithm in C++:

#include <iostream>
using namespace std;

int findMaxSubarraySum(int arr[], int size) {
    int max_so_far = 0;
    int max_ending_here = 0;

    for (int i = 0; i < size; i++) {
        max_ending_here = max_ending_here + arr[i];
        if (max_ending_here < 0) {
            max_ending_here = 0;
        }
        if (max_so_far < max_ending_here) {
            max_so_far = max_ending_here;
        }
    }

    return max_so_far;
}

int main() {
    int arr[] = {-2, -3, 4, -1, -2, 1, 5, -3};
    int size = sizeof(arr) / sizeof(arr[0]);

    int maxSum = findMaxSubarraySum(arr, size);
    cout << "Maximum sum of a contiguous subarray: " << maxSum << endl;

    return 0;
}

This implementation will output: Maximum sum of a contiguous subarray: 7, which corresponds to the maximum sum of the subarray {4, -1, -2, 1, 5}.