[NeetCode 150] Maximum Subarray

Maximum Subarray

Given an array of integers nums, find the subarray with the largest sum and return the sum.

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

Example 1:

Input: nums = [2,-3,4,-2,2,1,-1,4]

Output: 8

Explanation: The subarray [4,-2,2,1,-1,4] has the largest sum 8.

Example 2:

Input: nums = [-1]

Output: -1

Constraints:

1 <= nums.length <= 1000
-1000 <= nums[i] <= 1000

Solution

To compute the sum of a subarray, a commonly used method is to compute the difference between two prefix sum. For a given prefix, to get the maximum subarray, we need to find a minimum prefix before it. While we can maintain the minimum prefix sum in traverse, this problem can be done in $O(n)$ time complexity.

Code

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        minprefix = 0
        prefix = 0
        ans = nums[0]
        for num in nums:
            prefix += num
            ans = max(ans, prefix-minprefix)
            minprefix = min(prefix, minprefix)
        return ans