Multi-threaded Array Sort

Problem Statement

Given a large array of integers, implement a function to sort the array using multiple threads. Your solution should leverage parallelism to improve sorting performance over a single-threaded approach.

Examples

Example 1: Input: arr = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] Output: [1, 1, 2, 3, 3, 4, 5, 5, 5, 6, 9]

Example 2: Input: arr = [10, 5, 2, 3, 7, 6, 1, 8, 4] Output: [1, 2, 3, 4, 5, 6, 7, 8, 10]

Constraints

• 1 <= arr.length <= 10^6
• -10^9 <= arr[i] <= 10^9

Hints

1. Consider dividing the array into smaller subarrays and sorting each subarray in parallel using different threads.
2. After sorting each subarray, merge the sorted subarrays to obtain the final sorted array.

Solution

To solve this problem, you can follow these steps:

1. Divide the input array into smaller subarrays, each of which will be sorted by a separate thread.
2. Sort each subarray using a parallel sorting algorithm like parallel merge sort or parallel quicksort.
3. Merge the sorted subarrays to obtain the final sorted array.

Here's a high-level implementation in Python:

`python import threading

def parallel_sort(arr, low, high, result): if low < high: mid = (low + high) // 2 left_thread = threading.Thread(target=parallel_sort, args=(arr, low, mid, result)) right_thread = threading.Thread(target=parallel_sort, args=(arr, mid + 1, high, result))

    left_thread.start()
    right_thread.start()

    left_thread.join()
    right_thread.join()

    merge(arr, low, mid, high, result)

def merge(arr, low, mid, high, result): left = arr[low:mid + 1] right = arr[mid + 1:high + 1]

left_index = 0
right_index = 0
i = low

while left_index < len(left) and right_index < len(right):
    if left[left_index] <= right[right_index]:
        result[i] = left[left_index]
        left_index += 1
    else:
        result[i] = right[right_index]
        right_index += 1
    i += 1

while left_index < len(left):
    result[i] = left[left_index]
    left_index += 1
    i += 1

while right_index < len(right):
    result[i] = right[right_index]
    right_index += 1
    i += 1

def multi_threaded_sort(arr): result = [0] * len(arr) parallel_sort(arr, 0, len(arr) - 1, result) return result

Example usage:

arr = [3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5] sorted_arr = multi_threaded_sort(arr) print(sorted_arr) `

This solution divides the input array into smaller subarrays and sorts each subarray in parallel using separate threads. After sorting each subarray, it merges the sorted subarrays to obtain the final sorted array.