What is the optimal time complexity of solving Maximum Subarray?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Maximum Subarray?

The space complexity is O(n) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Maximum Subarray?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Maximum Subarray?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

Back to Practice Dashboard

Top 150 InterviewHard

Maximum Subarray

Learn how to solve the 'Maximum Subarray' problem. This detailed resource details brute force and optimized approaches.

Mode Selected

Problem Statement

Hard

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

Write a function maxSubArray(nums: List[int]) -> int.

Constraints

•1 <= len(nums) <= 10^5
•-10^4 <= nums[i] <= 10^4

Examples

Example 1

Input

nums = [-2,1,-3,4,-1,2,1,-5,4]

Output

Explanation

[4,-1,2,1] has the largest sum = 6.

Example 2

Input

nums = [1]

Output

Explanation

[1] has the largest sum = 1.

Need a Hint?

Analyze the input constraints. Try sorting first (O(n log n)) or using a hash map/set to track seen elements in O(n) time.

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

Ready to Solve?

Open the problem in PyRun's browser-based Python editor. Your code runs fully offline — no server required.

Open in Editor