Skip to content

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
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

        result = float('-inf')
        current_sum = 0
        for num in nums:
            current_sum += num
            if current_sum > result:
                result = current_sum
            if current_sum < 0:
                current_sum = 0

        return result

        # result = max_ending = nums[0]
        # for i in range(1, len(nums)):
        #     max_ending = max(max_ending + nums[i], nums[i])
        #     result = max(result, max_ending)

        # return result

Submission Stats:

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