Find Largest Sum Contiguous Subarray

Understanding the Problem

The goal is to find the subarray with the maximum sum in a given array using different methods.

Method 1: Kadane's Algorithm

This method efficiently finds the largest sum contiguous subarray using dynamic programming.

#include <iostream>
using namespace std;
int maxSubArraySum(int arr[], int size) {
    int max_so_far = arr[0], max_ending_here = arr[0];
    for (int i = 1; i < size; i++) {
        max_ending_here = max(arr[i], max_ending_here + arr[i]);
        max_so_far = max(max_so_far, max_ending_here);
    }
    return max_so_far;
}
int main() {
    int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    int size = sizeof(arr)/sizeof(arr[0]);
    cout << "Maximum contiguous sum: " << maxSubArraySum(arr, size);
    return 0;
}
            

Output:

Maximum contiguous sum: 6

Method 2: Divide and Conquer

This method finds the largest sum subarray by dividing the array into halves recursively.

#include <iostream>
using namespace std;
int maxCrossingSum(int arr[], int l, int m, int h) {
    int sum = 0, left_sum = -10000, right_sum = -10000;
    for (int i = m; i >= l; i--) {
        sum += arr[i];
        left_sum = max(left_sum, sum);
    }
    sum = 0;
    for (int i = m+1; i <= h; i++) {
        sum += arr[i];
        right_sum = max(right_sum, sum);
    }
    return max({left_sum + right_sum, left_sum, right_sum});
}
int maxSubArraySum(int arr[], int l, int h) {
    if (l == h) return arr[l];
    int m = (l + h) / 2;
    return max({maxSubArraySum(arr, l, m), maxSubArraySum(arr, m+1, h), maxCrossingSum(arr, l, m, h)});
}
int main() {
    int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    int size = sizeof(arr)/sizeof(arr[0]);
    cout << "Maximum contiguous sum: " << maxSubArraySum(arr, 0, size-1);
    return 0;
}
            

Output:

Maximum contiguous sum: 7

Method 3: Brute Force

This method checks all subarrays and computes their sums to find the maximum sum.

#include <iostream>
using namespace std;
int maxSubArraySum(int arr[], int size) {
    int max_sum = arr[0];
    for (int i = 0; i < size; i++) {
        int current_sum = 0;
        for (int j = i; j < size; j++) {
            current_sum += arr[j];
            max_sum = max(max_sum, current_sum);
        }
    }
    return max_sum;
}
int main() {
    int arr[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    int size = sizeof(arr)/sizeof(arr[0]);
    cout << "Maximum contiguous sum: " << maxSubArraySum(arr, size);
    return 0;
}
            

Output:

Maximum contiguous sum: 6