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

假设{ai, ai+1, …, aj, …ak}是满足要求的最大和子序列maxStr。那么如果maxStr的任一ai开头的子序列{ai …, aj}的和sum{ai …, aj} < 0，则maxStr的另一子序列sum{aj+1 …, ak} > sum{maxStr}。这与maxStr是最大和子序列矛盾。
因此， maxStr中任一ai开头的子序列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;    }};