LeetCode 053 Maximum Subarray

LeetCode

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

Constraints:

1 <= nums.length <= 10<sup>5</sup> -10<sup>4</sup> <= nums[i] <= 10<sup>4</sup>

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.

题目大意：

最大子数组和

算法思路：

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

注意事项：

1. 引入全局最大的res，因为递归式是以末位为结尾的最大和

Python代码：

# dp[i] = max(dp[i-1] + nums[i], nums[i])
def maxSubArray(self, nums: List[int]) -> int:
	sum, res = -sys.maxsize, -sys.maxsize
	for num in nums:
		if sum > 0:
			sum += num
		else:
			sum = num
		res = max(sum, res)
	return res

算法分析：

时间复杂度为O(n)，空间复杂度O(1)