LeetCode 53. Maximum Subarray（动态规划）

题目来源：https://leetcode.com/problems/maximum-subarray/

问题描述

53. Maximum Subarray

Easy

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.

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题意

经典的最大子段和问题。给定一个数列nums, 求最大的连续子段和。

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思路

动态规划，dp[i]表示以位置i结尾的连续子段的最大的和。

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代码

class Solution {
    public int maxSubArray(int[] nums) {
        int n = nums.length, i = 0, mymax = Integer.MIN_VALUE;
        if (n == 0)
        {
            return 0;
        }
        int[] dp = new int[n];  // dp[i]: max sum of contiguous subarray ended with index i
        dp[0] = nums[0];
        for (i=1; i<n; i++)
        {
            if (dp[i-1] <= 0)
            {
                dp[i] = nums[i];
            }
            else
            {
                dp[i] = dp[i-1] + nums[i];
            }
        }
        for (i=0; i<n; i++)
        {
            mymax = Math.max(mymax, dp[i]);
        }
        return mymax;
    }
}