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# Odd Even Transposition Sort / Brick Sort using pthreads

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, 10

Input: { 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

 `// CPP Program for Odd-Even Transposition sort``// using pthreads` `#include ``#include ` `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` `((index + 1 < n) && (a[index] > a[index + 1])) {``        ``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;``}`

## Python3

 `# Python3 Program for Odd-Even Transposition sort``# using pthreads``from` `threading ``import` `Thread` `# Size of array``N ``=` `8``# maximum number of threads``MAX_THREAD ``=` `int``((N``+``1``)``/``2``)``arr ``=` `[``2``, ``1``, ``4``, ``9``, ``5``, ``3``, ``6``, ``10``]``tmp ``=` `0` `# Function to compare and exchange``# the consecutive elements of the array``def` `compare():``    ``global` `tmp``    ``# Each thread compares``    ``# two consecutive elements of the array``    ``index ``=` `tmp``    ``tmp ``=` `tmp ``+` `2``    ``if` `index``+``1` `< N ``and` `arr[index] > arr[index``+``1``]:``        ``arr[index], arr[index``+``1``] ``=` `arr[index``+``1``], arr[index]`  `def` `createThreads():``    ``# creating list of size MAX_THREAD``    ``threads ``=` `list``(``range``(MAX_THREAD))``    ` `    ``# creating MAX_THEAD number of threads``    ``for` `index ``in` `range``(MAX_THREAD):``        ``threads[index] ``=` `Thread(target``=``compare)``        ``threads[index].start()``        ` `    ``# Waiting for all threads to finish``    ``for` `index ``in` `range``(MAX_THREAD):``        ``threads[index].join()`  `def` `oddEven():``    ``global` `tmp``    ``for` `i ``in` `range``(``1``, N``+``1``):``        ``# Odd Step``        ``if` `i ``%` `2``:``            ``tmp ``=` `0``            ``createThreads()``        ``# Even Step``        ``else``:``            ``tmp ``=` `1``            ``createThreads()` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``    ``print``(``"Given array is : %s"` `%` `arr)``    ``oddEven()``    ``print``(``"Sorted array is : %s"` `%` `arr)`

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).