53_MaximumSubarray.md

53. Maximum Subarray

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

A subarray is a contiguous part of an array.

Example 1:

Input: nums = [-2,1,-3,4,-1,2,1,-5,4]
Output: 6
Explanation: [4,-1,2,1] has the largest sum = 6.

Example 2:

Input: nums = [1]
Output: 1

Example 3:

Input: nums = [5,4,-1,7,8]
Output: 23

Clarification:

1 <= haystack.length, needle.length <= 104
haystack and needle consist of only lowercase English characters.

Solution:

• 解法一
  • 基本檢核過濾
  • 透過DP進行處理,動態的比對當前與之前sum的值進行比對

code:

• python

  class Solution:
      # 解法一
      def maxSubArray(self, nums: List[int]) -> int:
        if len(nums) <= 0:
            return 0
        if len(nums) == 1:
            return nums[0]
        dp = [0]*len(nums)
        for i, num in enumerate(nums):
            dp[i] = max(dp[i-1] + num, num)
        return max(dp)
  
      # 解法二