0053-maximum-subarray

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Description

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.

Solution(Python)

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
                # Initialize our variables using the first element.
        current_subarray = max_subarray = nums[0]

        # Start with the 2nd element since we already used the first one.
        for num in nums[1:]:
            # If current_subarray is negative, throw it away. Otherwise, keep adding to it.
            current_subarray = max(num, current_subarray + num)
            max_subarray = max(max_subarray, current_subarray)

        return max_subarray