53. Maximum Subarray

Problem

Given an integer array nums, find the subarray with the largest sum, and return its sum.

A subarray is a contiguous non-empty sequence of elements within an array.

https://leetcode.com/problems/maximum-subarray/

Example 1:

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

Example 2:

Input: nums = [1]
Output: 1
Explanation: The subarray [1] has the largest sum 1.

Example 3:

Input: nums = [5,4,-1,7,8]
Output: 23
Explanation: The subarray [5,4,-1,7,8] has the largest sum 23.

Constraints:

1 <= nums.length <= 10⁵
-10⁴ <= nums[i] <= 10⁴

Test Cases

1 2	class Solution: def maxSubArray(self, nums: List[int]) -> int:

solution_test.py

import pytest

from solution import Solution


@pytest.mark.parametrize('nums, expected', [
    ([-2,1,-3,4,-1,2,1,-5,4], 6),
    ([1], 1),
    ([5,4,-1,7,8], 23),
])
class Test:
    def test_solution(self, nums, expected):
        sol = Solution()
        assert sol.maxSubArray(nums) == expected

Thoughts

如果一个 subarray 的和大于 0，把它与下一个数相加的结果一定比下一个数自身大。反之，应该从下一个数开启新的 subarray。

记录当前 subarray 的总和，如果把下一个数加入进来，总和仍然大于 0，就可以继续。否则把 subarray 清空，总和恢复为 0，从再下一个数开始尝试建立新的 subarray。过程中记录见到的最大的总和。

Code

solution.py

from typing import List


class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        largest = nums[0]
        s = 0
        for v in nums:
            s += v
            largest = max(largest, s)
            s = max(s, 0)

        return largest

本文除了题目描述（Problem）部分之外，其他内容由 Calf 原创，采用 CC BY-NC-SA 4.0 许可协议，转载请注明出处。