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 <iostream> 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[0]); // 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 |
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:
- Find the maximum of the array and place it at the end of the array by
- Recursively call slowsort function for the maximum of the first N/2 elements.
- Recursively call slowsort function for the maximum of the remaining N/2 elements.
- Find the largest of that two maximum and store it at the end.
- Recursively call slowsort function for the entire array except for the maximum.
- Print the sorted array.
Below is the implementation of the above approach:
C++
// C++ program to implement Slow sort #include <bits/stdc++.h> 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[0]); // 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 |
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:
- 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.
- 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.
- 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 <Windows.h> #else // sleep() function for linux machine #include <unistd.h> #endif #include <iostream> #include <thread> #include <vector> 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[0]); // sleep_sort function call sleepSort(arr, N); return 0; } // To run compile using -pthread // { 1, 3, 4, 8, 9} |
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 <bits/stdc++.h> 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[0]); // 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; } |
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 <bits/stdc++.h> 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 permuatation // 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[0]; // Function Call bogosort(a, N); printf ( "Array after sorting:" ); printArray(a, N); return 0; } |
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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