LeetCode练题——53. Maximum Subarray

1、题目

53. Maximum Subarray——Easy

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.

2、我的解法

(1)超时的暴力解法

 1 # -*- coding: utf-8 -*-
 2 # @Time    : 2020/2/6 22:15
 3 # @Author  : SmartCat0929
 4 # @Email   : [email protected]
 5 # @Link    : https://github.com/SmartCat0929
 6 # @Site    : 
 7 # @File    : 53. Maximum Subarray(超时的暴力算法）.py
 8 from typing import List
 9 
10 
11 class Solution:
12     def maxSubArray(self, nums: List[int]) -> int:
13         maxSum = -9999999999
14         if len(nums)>1:
15             maxSum = -99999
16             for i in range(0, len(nums)):
17                 for j in range(i, len(nums)):
18                     thisSum = sum(nums[i:j+1])
19                     if thisSum > maxSum:
20                         maxSum = thisSum
21             return maxSum
22         elif len(nums)==1:
23             maxSum=nums[0]
24             return maxSum
25         else:
26             return 0
27 
28 print(Solution().maxSubArray([-2,1,-3,4,-1,2,1,-5,4]))

（2）局部最大值（copy大神）

 1 # -*- coding: utf-8 -*-
 2 # @Time    : 2020/2/7 16:12
 3 # @Author  : SmartCat0929
 4 # @Email   : [email protected]
 5 # @Link    : https://github.com/SmartCat0929
 6 # @Site    : 
 7 # @File    : 53. Maximum Subarray.py
 8 
 9 from typing import List
10 class Solution:
11     def maxSubArray(self, nums: List[int]) -> int:
12         n = len(nums)
13         tmp = 0
14         res = float('-inf')
15         for i in range(n):
16             if tmp < 0:
17                 tmp = 0
18             tmp = tmp + nums[i]
19             res = max(res, tmp)
20         return res
21 print(Solution().maxSubArray([-2,1,-3,4,-1,2,1,-5,4]))