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53. Maximum Subarray

Array Divide and Conquer Dynamic Programming

Problem - Maximum Subarray

Medium

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

 

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

 

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.

Solutions

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class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        result = dp = nums[0]
        for num in nums[1:]:
            dp = max(dp, 0) + num
            result = max(result, dp)
        return result

Submission Stats:

  • Runtime: 91 ms (30.37%)
  • Memory: 32.6 MB (43.33%)