[LeetCode] 53. Maximum Subarray

Posted 2021-02-18 arcsinw

Description

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.

Analyse

找出一个数组连续子序列的最大和

子序列要求连续，子序列向右扩展分为两种情况

1. 将新元素加入子序列，子序列长度+1
2. 抛弃之前的子序列，新元素成为新的子序列，子序列长度为1

子序列的局部最大和为这两种情况中和最大的那个

在所有的局部最大和中找出全局最大和

写出一个算法复杂度为(O(n))的版本

  def maxSubArray(self, nums: List[int]) -> int:
        maximum = nums[0]
        global_maximum = nums[0]

        for i in nums[1:]:
            maximum = max(maximum + i, i)
            global_maximum = max(maximum, global_maximum)

        return global_maximum