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

$a_i$	$a_{i+1}$	$...$	$a_j$	$...$	$a_{k-2}$	$a_{k-1}$	$a_k$

如果{$a_i$, $a_{i+1}$, …, $a_j$, …$a_k$}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的还有一子序列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;
    }
};

版权声明：本文博客原创文章，博客，未经同意，不得转载。