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# The Slowest Sorting Algorithms

• Difficulty Level : Easy
• Last Updated : 26 Jul, 2021

A Sorting Algorithm is used to rearrange a given array or list elements according to a comparison operator on the elements. The comparison operator is used to decide the new order of the element in the respective data structure. But Below is some of the slowest sorting algorithms:

Stooge Sort: A Stooge sort is a recursive sorting algorithm. It recursively divides and sorts the array in parts. Below are the steps of the Stooge Sort:

• If the value at index 0 is greater than the value at the last index, swap them.
• If the number of elements in the array is greater than two:
• Recursively call stoogesort function for the initial 2/3rd elements of the array.
• Recursively call stoogesort function for the last 2/3rd elements of the array.
• Recursively call stoogesort function for the initial 2/3rd elements again to confirm the resultant array is sorted or not.
• Print the sorted array.

Below is the implementation of the above approach:

## C++

 `// C++ program for the stooge sort``#include ``using` `namespace` `std;` `// Function to implement stooge sort``void` `stoogesort(``int` `arr[], ``int` `l, ``int` `h)``{``    ``// Base Case``    ``if` `(l >= h)``        ``return``;` `    ``// If first element is smaller than``    ``// last element, swap them``    ``if` `(arr[l] > arr[h])``        ``swap(arr[l], arr[h]);` `    ``// If there are more than 2 elements``    ``// in the array``    ``if` `(h - l + 1 > 2) {``        ``int` `t = (h - l + 1) / 3;` `        ``// Recursively sort the first``        ``// 2/3 elements``        ``stoogesort(arr, l, h - t);` `        ``// Recursively sort the last``        ``// 2/3 elements``        ``stoogesort(arr, l + t, h);` `        ``// Recursively sort the first``        ``// 2/3 elements again``        ``stoogesort(arr, l, h - t);``    ``}``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 2, 4, 5, 3, 1 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function Call``    ``stoogesort(arr, 0, N - 1);` `    ``// Display the sorted array``    ``for` `(``int` `i = 0; i < N; i++) {``        ``cout << arr[i] << ``" "``;``    ``}` `    ``return` `0;``}`

## Java

 `// Java program for the``// stooge sort``class` `GFG{``    ` `// Function to implement``// stooge sort``static` `void` `stoogesort(``int` `arr[],``                       ``int` `l, ``int` `h)``{``  ``// Base Case``  ``if` `(l >= h)``    ``return``;` `  ``// If first element is smaller``  ``// than last element, swap them``  ``if` `(arr[l] > arr[h])``  ``{``    ``int` `temp = arr[l];``    ``arr[l] = arr[h];``    ``arr[h] = temp;``  ``}` `  ``// If there are more than``  ``// 2 elements in the array``  ``if` `(h - l + ``1` `> ``2``)``  ``{``    ``int` `t = (h - l + ``1``) / ``3``;` `    ``// Recursively sort the``    ``// first 2/3 elements``    ``stoogesort(arr, l, h - t);` `    ``// Recursively sort the``    ``// last 2/3 elements``    ``stoogesort(arr, l + t, h);` `    ``// Recursively sort the``    ``// first 2/3 elements again``    ``stoogesort(arr, l, h - t);``  ``}``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ``int` `arr[] = {``2``, ``4``, ``5``, ``3``, ``1``};``  ``int` `N = arr.length;` `  ``// Function Call``  ``stoogesort(arr, ``0``, N - ``1``);` `  ``// Display the sorted array``  ``for` `(``int` `i = ``0``; i < N; i++)``  ``{``    ``System.out.print(arr[i] + ``" "``);``  ``}``}``}` `// This code is contributed by Chitranayal`

## Python3

 `# Python3 program for the stooge sort` `# Function to implement stooge sort``def` `stoogesort(arr, l, h):``    ` `    ``# Base Case``    ``if` `(l >``=` `h):``        ``return`` ` `    ``# If first element is smaller than``    ``# last element, swap them``    ``if` `(arr[l] > arr[h]):``        ``temp ``=` `arr[l]``        ``arr[l] ``=` `arr[h]``        ``arr[h] ``=` `temp` `    ``# If there are more than 2 elements``    ``# in the array``    ``if` `(h ``-` `l ``+` `1` `> ``2``):``        ``t ``=` `(h ``-` `l ``+` `1``) ``/``/` `3`` ` `        ``# Recursively sort the first``        ``# 2/3 elements``        ``stoogesort(arr, l, h ``-` `t)`` ` `        ``# Recursively sort the last``        ``# 2/3 elements``        ``stoogesort(arr, l ``+` `t, h)`` ` `        ``# Recursively sort the first``        ``# 2/3 elements again``        ``stoogesort(arr, l, h ``-` `t)``    ` `# Driver Code``arr ``=` `[ ``2``, ``4``, ``5``, ``3``, ``1` `]``N ``=` `len``(arr)`` ` `# Function Call``stoogesort(arr, ``0``, N ``-` `1``)` `# Display the sorted array``for` `i ``in` `range``(N):``    ``print``(arr[i], end ``=` `" "``)` `# This code is contributed by code_hunt`

## C#

 `// C# program for the``// stooge sort``using` `System;``class` `GFG{``    ` `// Function to implement``// stooge sort``static` `void` `stoogesort(``int` `[]arr,``                       ``int` `l, ``int` `h)``{``  ``// Base Case``  ``if` `(l >= h)``    ``return``;` `  ``// If first element is smaller``  ``// than last element, swap them``  ``if` `(arr[l] > arr[h])``  ``{``    ``int` `temp = arr[l];``    ``arr[l] = arr[h];``    ``arr[h] = temp;``  ``}` `  ``// If there are more than``  ``// 2 elements in the array``  ``if` `(h - l + 1 > 2)``  ``{``    ``int` `t = (h - l + 1) / 3;` `    ``// Recursively sort the``    ``// first 2/3 elements``    ``stoogesort(arr, l, h - t);` `    ``// Recursively sort the``    ``// last 2/3 elements``    ``stoogesort(arr, l + t, h);` `    ``// Recursively sort the``    ``// first 2/3 elements again``    ``stoogesort(arr, l, h - t);``  ``}``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``  ``int` `[]arr = {2, 4, 5, 3, 1};``  ``int` `N = arr.Length;` `  ``// Function Call``  ``stoogesort(arr, 0, N - 1);` `  ``// Display the sorted array``  ``for` `(``int` `i = 0; i < N; i++)``  ``{``    ``Console.Write(arr[i] + ``" "``);``  ``}``}``}` `// This code is contributed by Princi Singh`

## Javascript

 ``
Output:
`1 2 3 4 5`

Time Complexity: O(N2.709). Therefore, it is slower than even the Bubble Sort that has a time complexity of O(N2).

Slow Sort: The slow sort is an example of Multiply And Surrender a tongue-in-cheek joke of divide and conquer. Slow sort stores the maximum element of the array at the last position by recursively divides the array by half and compares each of them. Then it recursively calls the array without the previous maximum element and stores the new maximum element at the new last position. Below are the steps of Slow sort:

1. Find the maximum of the array and place it at the end of the array by
1. Recursively call slowsort function for the maximum of the first N/2 elements.
2. Recursively call slowsort function for the maximum of the remaining N/2 elements.
3. Find the largest of that two maximum and store it at the end.
4. Recursively call slowsort function for the entire array except for the maximum.
2. Print the sorted array.

Below is the implementation of the above approach:

## C++

 `// C++ program to implement Slow sort``#include ``using` `namespace` `std;` `// Function for swap two numbers using``// pointers``void` `swap(``int``* xp, ``int``* yp)``{``    ``int` `temp = *xp;``    ``*xp = *yp;``    ``*yp = temp;``}` `// Function that implements Slow Sort``void` `slowSort(``int` `A[], ``int` `i, ``int` `j)``{``    ``// Base Case``    ``if` `(i >= j)``        ``return``;` `    ``// Middle value``    ``int` `m = (i + j) / 2;` `    ``// Recursively call with left half``    ``slowSort(A, i, m);` `    ``// Recursively call with right half``    ``slowSort(A, m + 1, j);` `    ``// Swap if first element``    ``// is lower than second``    ``if` `(A[j] < A[m]) {``        ``swap(&A[j], &A[m]);``    ``}` `    ``// Recursively call with whole``    ``// array except maximum element``    ``slowSort(A, i, j - 1);``}` `// Function to print the array``void` `printArray(``int` `arr[], ``int` `size)``{``    ``int` `i;``    ``for` `(i = 0; i < size; i++)``        ``cout << arr[i] << ``" "``;``    ``cout << endl;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 6, 8, 9, 4, 12, 1 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function call``    ``slowSort(arr, 0, N - 1);` `    ``// Display the sorted array``    ``printArray(arr, N);` `    ``return` `0;``}`

## Java

 `// Java program to implement Slow sort``import` `java.util.*;` `class` `GFG``{` `// Function that implements Slow Sort``static` `void` `slowSort(``int` `A[], ``int` `i, ``int` `j)``{``    ``// Base Case``    ``if` `(i >= j)``        ``return``;` `    ``// Middle value``    ``int` `m = (i + j) / ``2``;` `    ``// Recursively call with left half``    ``slowSort(A, i, m);` `    ``// Recursively call with right half``    ``slowSort(A, m + ``1``, j);` `    ``// Swap if first element``    ``// is lower than second``    ``if` `(A[j] < A[m])``    ``{``        ``int` `temp = A[j];``        ``A[j] = A[m];``        ``A[m] = temp;``    ``}` `    ``// Recursively call with whole``    ``// array except maximum element``    ``slowSort(A, i, j - ``1``);``}` `// Function to print the array``static` `void` `printArray(``int` `arr[], ``int` `size)``{``    ``int` `i;``    ``for` `(i = ``0``; i < size; i++)``        ``System.out.print(arr[i]+ ``" "``);``    ``System.out.println();``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``6``, ``8``, ``9``, ``4``, ``12``, ``1` `};``    ``int` `N = arr.length;` `    ``// Function call``    ``slowSort(arr, ``0``, N - ``1``);` `    ``// Display the sorted array``    ``printArray(arr, N);``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python program to implement Slow sort` `# Function that implements Slow Sort``def` `slowSort(A, i, j):``  ` `    ``# Base Case``    ``if` `(i >``=` `j):``        ``return``;` `    ``# Middle value``    ``m ``=` `(i ``+` `j) ``/``/` `2``;` `    ``# Recursively call with left half``    ``slowSort(A, i, m);` `    ``# Recursively call with right half``    ``slowSort(A, m ``+` `1``, j);` `    ``# Swap if first element``    ``# is lower than second``    ``if` `(A[j] < A[m]):``        ``temp ``=` `A[j];``        ``A[j] ``=` `A[m];``        ``A[m] ``=` `temp;` `    ``# Recursively call with whole``    ``# array except maximum element``    ``slowSort(A, i, j ``-` `1``);` `# Function to prthe array``def` `printArray(arr, size):``    ``i ``=` `0``;``    ``for` `i ``in` `range``(size):``        ``print``(arr[i], end``=``" "``);``    ``print``();` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ``arr ``=` `[``6``, ``8``, ``9``, ``4``, ``12``, ``1``];``    ``N ``=` `len``(arr);` `    ``# Function call``    ``slowSort(arr, ``0``, N ``-` `1``);` `    ``# Display the sorted array``    ``printArray(arr, N);` `    ``# This code contributed by gauravrajput1`

## C#

 `// C# program to implement Slow sort``using` `System;``class` `GFG``{` `// Function that implements Slow Sort``static` `void` `slowSort(``int` `[]A, ``int` `i, ``int` `j)``{``    ``// Base Case``    ``if` `(i >= j)``        ``return``;` `    ``// Middle value``    ``int` `m = (i + j) / 2;` `    ``// Recursively call with left half``    ``slowSort(A, i, m);` `    ``// Recursively call with right half``    ``slowSort(A, m + 1, j);` `    ``// Swap if first element``    ``// is lower than second``    ``if` `(A[j] < A[m])``    ``{``        ``int` `temp = A[j];``        ``A[j] = A[m];``        ``A[m] = temp;``    ``}` `    ``// Recursively call with whole``    ``// array except maximum element``    ``slowSort(A, i, j - 1);``}` `// Function to print the array``static` `void` `printArray(``int` `[]arr, ``int` `size)``{``    ``int` `i;``    ``for` `(i = 0; i < size; i++)``        ``Console.Write(arr[i] + ``" "``);``    ``Console.WriteLine();``}` `// Driver Code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 6, 8, 9, 4, 12, 1 };``    ``int` `N = arr.Length;` `    ``// Function call``    ``slowSort(arr, 0, N - 1);` `    ``// Display the sorted array``    ``printArray(arr, N);``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:
`1 4 6 8 9 12`

Time Complexity:

• Base Case: O(N((log N)/(2+e)) where, e > 0
• Average Case: O(N(log(N)/2))

Even the best case is worse than Bubble sort. It is less efficient than Stooge sort.

Sleep Sort: Below is the steps of Stooge sort:

1. Create different threads for each of the elements in the input array and then each thread sleeps for an amount of time which is proportional to the value of the corresponding array element.
2. The thread having the least amount of sleeping time wakes up first and the number gets printed and then the second least element and so on.
3. The largest element wakes up after a long time and then the element gets printed at the last. Thus, the output is a sorted one.

All this Multithreading process happens in the background and at the core of the OS

Below is the implementation of the above approach:

## C++

 `// C++ program to implement Sleep sort``#ifdef _WIN32` `// sleep() function for windows machine``#include ``#else` `// sleep() function for linux machine``#include ``#endif``#include ``#include ``#include ` `using` `namespace` `std;` `// Array for storing the sorted values``vector<``int``> A;` `// Function for print the array``void` `printArray(vector<``int``> arr, ``int` `size)``{``    ``int` `i;``    ``for` `(i = 0; i < size; i++) {``        ``cout << arr[i] << ``" "``;``    ``}``}` `// The instruction set for a thread``void` `add(``int` `x)``{``    ``// Temporarily suspend execution``    ``// of each thread for x amount``    ``// of seconds``    ``sleep(x);` `    ``// Every thead will wake up after``    ``// a particular time and push the``    ``// value in sorted array``    ``A.push_back(x);``}` `// Function for Sleep sort``void` `sleepSort(``int` `arr[], ``int` `N)``{` `    ``vector<``thread``> threads;``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// New threads were launched by``        ``// using function pointer as``        ``// callable``        ``threads.push_back(``            ``thread``(add, arr[i]));``    ``}` `    ``// Waiting for each thread``    ``// to finish execution``    ``for` `(``auto``& th : threads) {``        ``th.join();``    ``}` `    ``// Display the sorted array``    ``cout << ``"Array after sorting: "``;``    ``printArray(A, A.size());``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 8, 9, 1, 4, 3 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// sleep_sort function call``    ``sleepSort(arr, N);` `    ``return` `0;``}` `// To run compile using -pthread``// {  1, 3, 4, 8, 9}`
Output:
`Array after sorting 1 3 4 8 9`

Time Complexity: O(max(input) + N) where, input = value of array element

Other algorithm’s time complexity depends upon the number of data but for sleep sort, it depends on the amount of data. This algorithm won’t work for negative numbers as a thread cannot sleep for a negative amount of time.

Bogo Sort: Two versions of this algorithm exist: one enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.

Example 1:

## C++

 `// C++ program to implement Bogo Sort``// using permutation``#include ``using` `namespace` `std;` `// Function to sort array using bogosort``void` `bogosort(``int` `arr[], ``int` `N)``{``    ``// Run the loop until``    ``// array is not sorted``    ``while` `(!is_sorted(arr, arr + N)) {` `        ``// All possible permutations``        ``next_permutation(arr, arr + N);``    ``}``}``// Driver Code``int` `main()``{` `    ``int` `arr[] = { 8, 9, 1, 4, 3 };` `    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``// Function Call``    ``bogosort(arr, N);` `    ``// Display the sorted array``    ``cout << ``"Array after sorting "``;``    ``for` `(``int` `i = 0; i < N; ++i) {``        ``cout << arr[i] << ``" "``;``    ``}``    ``cout << endl;` `    ``return` `0;``}`
Output:
`Array after sorting 1 3 4 8 9`

Time Complexity:

• Base Case: O(N)
• Average Case: O(N!)
• Worst Case: O(N!)

Example 2:

## C++

 `// C++ program to implement Bogo Sort``// using random shuffle``#include ``using` `namespace` `std;` `// Function to check if array is``// sorted or not``bool` `isSorted(``int` `a[], ``int` `N)``{``    ``while` `(--N > 1) {` `        ``// Break condition for``        ``// unsorted array``        ``if` `(a[N] < a[N - 1])``            ``return` `false``;``    ``}``    ``return` `true``;``}` `// Function to generate permutation``// of the array``void` `shuffle(``int` `a[], ``int` `N)``{``    ``for` `(``int` `i = 0; i < N; i++)``        ``swap(a[i], a[``rand``() % N]);``}` `// Function to sort array using``// Bogo sort``void` `bogosort(``int` `a[], ``int` `N)``{``    ``// If array is not sorted``    ``// then shuffle array again``    ``while` `(!isSorted(a, N)) {` `        ``shuffle(a, N);``    ``}``}` `// Function to print the array``void` `printArray(``int` `a[], ``int` `N)``{``    ``for` `(``int` `i = 0; i < N; i++) {` `        ``printf``(``"%d "``, a[i]);``    ``}``    ``printf``(``"\n"``);``}` `// Driver Code``int` `main()``{``    ``int` `a[] = { 3, 2, 5, 1, 0, 4 };``    ``int` `N = ``sizeof` `a / ``sizeof` `a;` `    ``// Function Call``    ``bogosort(a, N);``    ``printf``(``"Array after sorting:"``);``    ``printArray(a, N);``    ``return` `0;``}`
Output:
`Array after sorting:0 1 2 3 4 5`

Time Complexity:

• Base Case: O(N)
• Average Case: O(N*N!)
• Worst Case: O(∞)

Clearly, in the worst situation, Bogo sort using random shuffle takes an infinite amount of time to sort an array, and we may say that this is the slowest sorting algorithm. But the thing about Bogo Sort is that it violates some rules in Complexity Analysis. One of the rules is that you actually have to progress towards a goal. You can’t just obviously waste time for example by putting delay loops. The Slow Sort or stooge sort algorithm actually never makes a wrong move. Once it swaps two nodes the nodes will be in the correct order relative to each other and their order will not be reversed.

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