leetcode -- Maximum Subarray

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.

分析

假设{$a_i$, $a_{i+1}$, …, $a_j$, …$a_k$}是满足要求的最大和子序列maxStr。那么如果maxStr的任一$a_i$开头的子序列{$a_i$ …, $a_j$}的和sum{$a_i$ …, $a_j$} < 0，则maxStr的另一子序列sum{$a_{j+1}$ …, $a_k$} > sum{maxStr}。这与maxStr是最大和子序列矛盾。
因此， maxStr中任一$a_i$开头的子序列sum{$a_i$ …, $a_j$} $\ge$ 0.

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