LeetCode

Maximum Subarray

2013.12.17 14:21

Find the contiguous subarray within an array (containing at least one number) which has the largest sum.

For example, given the array [−2,1,−3,4,−1,2,1,−5,4],
the contiguous subarray [4,−1,2,1] has the largest sum = 6.

click to show more practice.

More practice:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

Solution:

　　This is a typical problem on any Data Structure textbook. Need no further explanation.

　　Time complexity is O(n), space complexity O(1).

Accepted code:

//#define __MAIN__
#include <cstdio>
#include <cstdlib>
using namespace std;

class Solution {
public:
    int maxSubArray(int A[], int n) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        if(A == nullptr){
            return 0;
        }

        if(n <= 0){
            return 0;
        }

        int i;
        int max_value;

        max_value = A[0];
        for(i = 0; i < n; ++i){
            if(A[i] > max_value){
                max_value = A[i];
            }
            if(A[i] >= 0){
                break;
            }
        }

        if(i >= n && max_value <= 0){
            // All A[i]s are 0 or negative.
            return max_value;
        }

        int sum, max_sum;

        sum = max_sum = 0;
        for(i = 0; i < n; ++i){
            sum += A[i];
            if(sum < 0){
                sum = 0;
            }
            if(sum > max_sum){
                max_sum = sum;
            }
        }

        return max_sum;
    }
};

#ifdef __MAIN__
int main()
{
    Solution sol;
    int A[] = {-2, 1, -3, 4, -1, 2, 1, -5, 4};
    const int n = sizeof(A) / sizeof(int);

    printf("%d
", sol.maxSubArray(A, n));

    return 0;
}
#endif