【每日一题leetcode】53. Maximum Subarray

Cecilia-Casper

于 2018-06-25 17:54:54 发布

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本文介绍了求解最大子数组和问题的一种高效算法——Kadane's Algorithm，并通过实例[-2,1,-3,4,-1,2,1,-5,4]展示了如何使用该算法找到具有最大和的连续子数组。通过对原始双循环方法的优化，实现了更简洁高效的代码实现。

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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.

最开始用了两个循环，之后参考了讨论区的解决方案，学习到了Kadane’s Algorithm。优化后代码如下

class Solution:
    def maxSubArray(self, nums):
        """
        :type nums: List[int]
        :rtype: int
        """
        lengh = len(nums)
        if lengh == 1:
            return nums[0]
        
        maxsum = temp = nums[0]
        for i in range(1,lengh):
            temp = max(nums[i],temp+nums[i])    #Kadane’s Algorithm maxSum = max(A[i],A[i]+maxSum)
            maxsum = max(maxsum,temp)
            

            
        
        return maxsum

参考：

http://theoryofprogramming.com/2016/10/21/dynamic-programming-kadanes-algorithm/

https://leetcode.com/problems/maximum-subarray/discuss/20193/DP-solution-and-some-thoughts