Maximum Subarray

Dynamic Programming

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.

 

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.

C++实现代码：

#include<iostream>
#include<climits>
using namespace std;

class Solution {
public:
    int maxSubArray(int A[], int n) {
        if(n==0)
            return 0;
        int maxSum=0;
        int sum=0;
        int i;
        int max=INT_MIN;
        for(i=0;i<n;i++)
        {
            if(A[i]>=0)
               break;
            if(A[i]>max)
                max=A[i];
        }
        if(i>=n)
            return max;
        for(i=0;i<n;i++)
        {
            sum+=A[i];
            if(maxSum<sum)
            {
                maxSum=sum;
            }
            if(sum<0)
                sum=0;
        }
        return maxSum;
    }
};

int main()
{
    Solution s;
    int A[10]={-2,-3,-8,0};
    cout<<s.maxSubArray(A,10)<<endl;
}

注意：其中至少包含一个数，所以当全是负数时，只能返回最大的负数。。