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

ai	ai+1	...	aj	...	ak−2	ak−1	ak

假設{ai , ai+1 , …, aj , …ak }是滿足要求的最大和子序列maxStr。那麼如果maxStr的任一ai 開頭的子序列{ai …, aj }的和sum{ai …, aj } < 0，則maxStr的另一子序列sum{aj+1 …, ak } > sum{maxStr}。這與maxStr是最大和子序列矛盾。
因此， maxStr中任一ai 開頭的子序列sum{ai …, aj } ≥ 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;
    }
};