Maximum Subarray

Maximum Subarray

Given an integer array nums, find the contiguous subarray (containing at least one number) which has the largest sum and return its sum.

A subarray is a contiguous part of an array.

Examples

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 <= 10^5
• -10^4 <= nums[i] <= 10^4

Expected Complexity

• Time: O(n). single pass through the array
• Space: O(1). only a constant number of variables