Daily LeetCode 53. Maximum Subarray

https://leetcode.com/problems/maximum-subarray/

Medium

问题描述

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.

思路及代码：

给定一个数组，求和最大的子串。

动态规划：

虽然这一题也是要求子串的问题，但是跟昨天的不同，我们不需要维护二维数组，因为这条题目的最终目的是求和。

我们只需要一个一维数组dp，dp[i]表示nums[0:i]的最大和，状态转移方程：dp[i]=max(dp[i-1] + nums[i], nums[i])

代码：

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        dp = [0] * len(nums)
        for i in range(len(nums)):
			dp[i] = max(dp[i-1] + nums[i], nums[i])

        return max(dp)

我们可以维护一个变量tmp_ans以节省空间，在遍历过程中判断tmp_ans是否小于零，若小于零，则重置tmp_ans为0，即改变求和起点，重新求和。

import sys
class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        max_sum = -sys.maxsize - 1
        tmp_ans = 0
        for i in range(len(nums)):
            if tmp_ans < 0: tmp_ans = 0
            tmp_ans += nums[i]
            max_sum = max(tmp_ans, max_sum)

        return max_sum