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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
Updated on: 21-Oct-2019
307 Views
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