53 Maximum Subarray - Medium

Problem:

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.

Problem Analysis:

• use greedy approach; specifically Kadene's Algorithm

Solutions:

class Solution:
    def maxSubArray(self, nums: List[int]) -> int:
        # max_so_far: overall maximum sum found in the array up to the current position in the iteration.
        # max_ending_here: maximum sum of subarrays that include the current element
        max_so_far = max_ending_here = nums[0]

        for num in nums[1:]:
            max_ending_here = max(num, max_ending_here + num)
            max_so_far = max(max_so_far, max_ending_here)

        return max_so_far        

Similar Questions