leetcode——[053]Maximum Subarray最大子序和

题目

给定一个整数数组 nums ，找到一个具有最大和的连续子数组（子数组最少包含一个元素），返回其最大和。

示例:

输入: [-2,1,-3,4,-1,2,1,-5,4],
输出: 6
解释: 连续子数组 [4,-1,2,1] 的和最大，为 6。

进阶:

如果你已经实现复杂度为 O(n) 的解法，尝试使用更为精妙的分治法求解。

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

Example:

Input: [-2,1,-3,4,-1,2,1,-5,4],
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

Follow up:

If you have figured out the O(n) solution, try coding another solution using the divide and conquer approach, which is more subtle.

解题方法

动态规划，前 $i$ 个整数的最大自序等于{前 $i-1$ 个整数的最大自序和，前 $i$ 个整数末尾最大子自序和}中的较大值。这段代码跑了2ms，超过了100%的Java提交。

public class Solution {
    // Method 1 2ms 100%
    public int maxSubArray(int[] nums) {
        int max = nums[0];    // store current maxinum 
        int tail = max;    // store the maxinum of tail subarray
        for (int i = 1; i < nums.length; i++) {
            tail = tail < 0 ? nums[i] : tail + nums[i];
            max = tail > max ? tail : max;
        }
        return max;
    }
}