leetcode 53. Maximum Subarray

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题目

  1. Maximum Subarray Easy

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Share 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

思路:动态规划

1.问题拆解:

以i为结尾的所有字数组中,和最大的是多少

2.状态定义:

dp[i]i为结尾的所有子数组的最大值

3.递推方程推导

dp[i]=max(dp[i-1]+array[i],array[i])

4.实现

实现

代码:python3

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

if __name__ == '__main__':
    print(Solution().maxSubArray([-2,1,-3,4,-1,2,1,-5,4])) 

参考

参考:mp.weixin.qq.com/s?__biz=MzU…