What is the optimal time complexity of solving Merge Sort?

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

What is the auxiliary space complexity for Merge Sort?

The space complexity is O(1) 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 Merge Sort?

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 Merge Sort?

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

DSA SectionEasy

Merge Sort

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

Mode Selected

Problem Statement

Easy

Write a function merge_sort(arr) that sorts a list of integers arr in ascending order using the Merge Sort algorithm and returns the sorted list.

Constraints

•0 <= len(arr) <= 10^4
•-10^5 <= arr[i] <= 10^5

Examples

Example 1

Input

arr = [38, 27, 43, 3, 9, 82, 10]

Output

[3, 9, 10, 27, 38, 43, 82]

Explanation

The list is divided in half recursively, sorted, and then merged back together.

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