Odd-Even Transposition Sort is a parallel sorting algorithm. It is based on the Bubble Sort technique, which compares every 2 consecutive numbers in the array and swap them if first is greater than the second to get an ascending order array. It consists of 2 phases – the odd phase and even phase:

**Odd phase:**Every odd indexed element is compared with the next even indexed element(considering 1-based indexing).**Even phase:**Every even indexed element is compared with the next odd indexed element.

This article uses the concept of multi-threading, specifically pthread. In each iteration, every pair of 2 consecutive elements is compared using individual threads executing in parallel as illustrated below.

**Examples:**

Input:{ 2, 1, 4, 9, 5, 3, 6, 10 }Output:1, 2, 3, 4, 5, 6, 9, 10Input:{ 11, 19, 4, 20, 1, 22, 25, 8}Output:1, 4, 8, 11, 19, 20, 22, 25

**Note:** Compile the program using following command on your Linux based system.

g++ program_name.cpp -pthread

Below is the implementation of the above topic:

`// CPP Program for Odd-Even Transpostion sort` `// using pthreads` ` ` `#include <bits/stdc++.h>` `#include <pthread.h>` ` ` `using` `namespace` `std;` ` ` `// size of array` `#define n 8` ` ` `// maximum number of threads` `int` `max_threads = (n + 1) / 2;` ` ` `int` `a[] = { 2, 1, 4, 9, 5, 3, 6, 10 };` `int` `tmp;` ` ` `// Function to compare and exchange` `// the consecutive elements of the array` `void` `* compare(` `void` `* arg)` `{` ` ` ` ` `// Each thread compares` ` ` `// two consecutive elements of the array` ` ` `int` `index = tmp;` ` ` `tmp = tmp + 2;` ` ` ` ` `if` `((a[index] > a[index + 1]) && (index + 1 < n)) {` ` ` `swap(a[index], a[index + 1]);` ` ` `}` `}` ` ` `void` `oddEven(pthread_t threads[])` `{` ` ` `int` `i, j;` ` ` ` ` `for` `(i = 1; i <= n; i++) {` ` ` `// Odd step` ` ` `if` `(i % 2 == 1) {` ` ` `tmp = 0;` ` ` ` ` `// Creating threads` ` ` `for` `(j = 0; j < max_threads; j++)` ` ` `pthread_create(&threads[j], NULL, compare, NULL);` ` ` ` ` `// joining threads i.e. waiting` ` ` `// for all the threads to complete` ` ` `for` `(j = 0; j < max_threads; j++)` ` ` `pthread_join(threads[j], NULL);` ` ` `}` ` ` ` ` `// Even step` ` ` `else` `{` ` ` `tmp = 1;` ` ` ` ` `// Creating threads` ` ` `for` `(j = 0; j < max_threads - 1; j++)` ` ` `pthread_create(&threads[j], NULL, compare, NULL);` ` ` ` ` `// joining threads i.e. waiting` ` ` `// for all the threads to complete` ` ` `for` `(j = 0; j < max_threads - 1; j++)` ` ` `pthread_join(threads[j], NULL);` ` ` `}` ` ` `}` `}` ` ` `// Function to print an array` `void` `printArray()` `{` ` ` `int` `i;` ` ` `for` `(i = 0; i < n; i++)` ` ` `cout << a[i] << ` `" "` `;` ` ` `cout << endl;` `}` ` ` `// Driver Code` `int` `main()` `{` ` ` ` ` `pthread_t threads[max_threads];` ` ` ` ` `cout << ` `"Given array is: "` `;` ` ` `printArray();` ` ` ` ` `oddEven(threads);` ` ` ` ` `cout << ` `"\nSorted array is: "` `;` ` ` `printArray();` ` ` ` ` `return` `0;` `}` |

**Output:**

Given array is: 2 1 4 9 5 3 6 10 Sorted array is: 1 2 3 4 5 6 9 10

**Time complexity**: The time complexity is reduced to O(N) due to parallel computation using threads.**Work complexity**: The work complexity of this program is O(N) as N/2 number of threads(resources) are being used to sort the array. So, the work-time complexity of the program is O(N^2).

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