Implement a parallelized sort
Company: xAI
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Onsite
## Problem: Parallelized Sort (Shared-Memory)
Implement a function that sorts an array using **parallelism**.
### Task
Write a function (language of your choice) with the following signature:
- `parallelSort(arr, numWorkers) -> sortedArr`
Where:
- `arr` is an array of integers (may contain duplicates and negative values).
- `numWorkers` is the maximum number of worker threads/tasks you may use.
- You may use basic concurrency primitives from the standard library (threads, thread pools, futures, barriers, mutexes, etc.).
- Do **not** rely on a built-in “parallel sort” library call.
### Requirements
1. **Correctness:** Return `arr` sorted in non-decreasing order.
2. **Parallelization:** The algorithm must perform meaningful work in parallel when `numWorkers > 1`.
3. **Resource limits:** Do not spawn more than `numWorkers` concurrent workers.
4. **Performance awareness:** Avoid parallel overhead for small subproblems (use a threshold where work switches to a sequential sort).
### Input / Output
- **Input:** `arr` (length `n`), `numWorkers`.
- **Output:** The sorted array (in-place or as a new array—state your choice).
### Constraints (assume for design)
- `1 <= n <= 1e6`
- `1 <= numWorkers <= 32`
- Aim for time complexity close to `O(n log n)` and reasonable memory usage.
### Follow-ups (if time)
- How would you choose the sequential cutoff threshold?
- How would you handle very large arrays where memory allocation during merge becomes expensive?
- How would you test that the implementation is thread-safe and actually parallel?
Quick Answer: This question evaluates understanding of parallel algorithms, shared-memory concurrency primitives, synchronization, workload partitioning, and performance trade-offs such as parallel overhead and resource limits.
You are given an array of integers and an integer `workers` representing how many parallel workers you *could* use. Implement a **parallelizable sorting algorithm**: split the array into `workers` chunks, sort each chunk independently, then merge the sorted chunks into one fully sorted array.
Although this function runs in a single process for this exercise, your algorithm must follow the parallel-sort structure (chunking + per-chunk sort + k-way merge), not simply call `sorted(nums)` on the whole list.
Return the array sorted in non-decreasing (ascending) order.
Constraints
- 0 <= len(nums) <= 200000
- -10^9 <= nums[i] <= 10^9
- 1 <= workers <= 100000
- Your algorithm must split into chunks, sort each chunk, then k-way merge
Examples
Input: ([3, 1, 2], 2)
Expected Output: [1, 2, 3]
Explanation: Split into chunks, sort each, then merge to get ascending order.
Input: ([1, 2, 3, 4, 5], 3)
Expected Output: [1, 2, 3, 4, 5]
Explanation: Already sorted; chunk sorting and merge preserve order.
Input: ([0, -1, 5, 3, 3, -1], 4)
Expected Output: [-1, -1, 0, 3, 3, 5]
Explanation: Handles negatives and duplicates correctly.
Input: ([10, 9, 8], 10)
Expected Output: [8, 9, 10]
Explanation: When workers > n, chunk size becomes 1; merging still works.
Input: ([], 5)
Expected Output: []
Explanation: Empty input returns empty output.