BogoSort or Permutation Sort

BogoSort also known as permutation sort, stupid sort, slow sort, shotgun sort or monkey sort is a particularly ineffective algorithm one person can ever imagine. It is based on generate and test paradigm. The algorithm successively generates permutations of its input until it finds one that is sorted.(Wiki) For example, if bogosort is used to sort a deck of cards, it would consist of checking if the deck were in order, and if it were not, one would throw the deck into the air, pick the cards up at random, and repeat the process until the deck is sorted.

Algorithm:

Bogo sort uses 2 steps to sort elements of the array.
1. It throws the number randomly.
2. Check whether the number is sorted or not.
3. If sorted then return the sorted array.
4. Otherwise it again generate another randomization of the numbers until the array is sorted.

PseudoCode:

while not Sorted(list) do
    shuffle (list)
done

Example: Let us consider an example array ( 3 2 5 1 0 4 ) 4 5 0 3 2 1 (1st shuffling) 4 1 3 2 5 0 (2ndshuffling) 1 0 3 2 5 4 (3rd shuffling) 3 1 0 2 4 5 (4th shuffling) 1 4 5 0 3 2 (5th shuffling) . . . 0 1 2 3 4 5 (nth shuffling)—— Sorted Array Here, n is unknown because algorithm doesn’t know in which step the resultant permutation will come out to be sorted. 

C++

// C++ implementation of Bogo Sort
#include <bits/stdc++.h>
using namespace std;

// To check if array is sorted or not
bool isSorted(int a[], int n)
{
    while (--n > 1)
        if (a[n] < a[n - 1])
            return false;
    return true;
}

// 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]);
}

// Sorts array a[0..n-1] using Bogo sort
void bogosort(int a[], int n)
{
    // if array is not sorted then shuffle
    // the array again
    while (!isSorted(a, n))
        shuffle(a, n);
}

// prints the array
void printArray(int a[], int n)
{
    for (int i = 0; i < n; i++)
        cout << a[i] << " ";
    cout << "\n";
}

// Driver code
int main()
{
    int a[] = { 3, 2, 5, 1, 0, 4 };
    int n = sizeof a / sizeof a[0];
    bogosort(a, n);
    printf("Sorted array :\n");
    printArray(a, n);
    return 0;
}

Java

// Java Program to implement BogoSort
public class BogoSort {
    // Sorts array a[0..n-1] using Bogo sort
    void bogoSort(int[] a)
    {
        // if array is not sorted then shuffle the
        // array again
        while (isSorted(a) == false)
            shuffle(a);
    }

    // To generate permutation of the array
    void shuffle(int[] a)
    {
        // Math.random() returns a double positive
        // value, greater than or equal to 0.0 and
        // less than 1.0.
        for (int i = 1; i < a.length; i++)
            swap(a, i, (int)(Math.random() * i));
    }

    // Swapping 2 elements
    void swap(int[] a, int i, int j)
    {
        int temp = a[i];
        a[i] = a[j];
        a[j] = temp;
    }

    // To check if array is sorted or not
    boolean isSorted(int[] a)
    {
        for (int i = 1; i < a.length; i++)
            if (a[i] < a[i - 1])
                return false;
        return true;
    }

    // Prints the array
    void printArray(int[] arr)
    {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    public static void main(String[] args)
    {
        // Enter array to be sorted here
        int[] a = { 3, 2, 5, 1, 0, 4 };
        BogoSort ob = new BogoSort();

        ob.bogoSort(a);

        System.out.print("Sorted array: ");
        ob.printArray(a);
    }
}

Python

# Python program for implementation of Bogo Sort
import random

# Sorts array a[0..n-1] using Bogo sort


def bogoSort(a):
    n = len(a)
    while (is_sorted(a) == False):
        shuffle(a)

# To check if array is sorted or not


def is_sorted(a):
    n = len(a)
    for i in range(0, n-1):
        if (a[i] > a[i+1]):
            return False
    return True

# To generate permutation of the array


def shuffle(a):
    n = len(a)
    for i in range(0, n):
        r = random.randint(0, n-1)
        a[i], a[r] = a[r], a[i]


# Driver code to test above
a = [3, 2, 4, 1, 0, 5]
bogoSort(a)
print("Sorted array :")
for i in range(len(a)):
    print("%d" % a[i]),

C#

// C# implementation of Bogo Sort
using System;

class GFG {
    // To Swap two given numbers
    static void Swap<T>(ref T lhs, ref T rhs)
    {
        T temp;
        temp = lhs;
        lhs = rhs;
        rhs = temp;
    }

    // To check if array is sorted or not
    public static bool isSorted(int[] a, int n)
    {
        int i = 0;
        while (i < n - 1) {
            if (a[i] > a[i + 1])
                return false;
            i++;
        }
        return true;
    }

    // To generate permutation of the array
    public static void shuffle(int[] a, int n)
    {
        Random rnd = new Random();
        for (int i = 0; i < n; i++)
            Swap(ref a[i], ref a[rnd.Next(0, n)]);
    }

    // Sorts array a[0..n-1] using Bogo sort
    public static void bogosort(int[] a, int n)
    {
        // if array is not sorted then shuffle
        // the array again
        while (!isSorted(a, n))
            shuffle(a, n);
    }

    // prints the array
    public static void printArray(int[] a, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write(a[i] + " ");
        Console.Write("\n");
    }

    // Driver code
    static void Main()
    {
        int[] a = { 3, 2, 5, 1, 0, 4 };
        int n = a.Length;
        bogosort(a, n);
        Console.Write("Sorted array :\n");
        printArray(a, n);
    }
    // This code is contributed by DrRoot_
}

Javascript

<script>
    // Javascript program for implementation of Bogo sort

    // To check if array is sorted or not
    function isSorted(a, n){
        for(var i = 1; i < arr.length; i++)
            if (a[i] < a[i-1])
                return false;
        return true;
    }

    //swap function
    function swap(arr, xp, yp){
        var temp = arr[xp];
        arr[xp] = arr[yp];
        arr[yp] = temp;
    }

    // To generate permutation of the array
    function shuffle(a, n){
        var i, j=n;
        for (i=0; i < n; i++){
            var ind = Math.floor(Math.random() * n);
            swap(a, j-i-1, ind);
        }
        return a;
    }

    // Sorts array a[0..n-1] using Bogo sort
    function bogosort(a, n){
        // if array is not sorted then shuffle
        // the array again
        while (!isSorted(a, n))
            a = shuffle(a, n);
        return a;
    }

    // prints the array
    function printArray(arr, size){
        var i;
        for (i=0; i < size; i++)
            document.write(arr[i]+ " ");
        document.write("\n");
    }

    // Driver code
    var arr = [3, 2, 5, 1, 0, 4];
    var n = arr.length;
    arr = bogosort(arr, n);
    document.write("Sorted array: \n");
    printArray(arr, n);

    // This code is contributed by Susobhan Akhuli
</script>

Output

Sorted array :
0 1 2 3 4 5 

Time Complexity: 

• Worst Case : O(∞) (since this algorithm has no upper bound)
• Average Case: O(n*n!)
• Best Case : O(n)(when array given is already sorted)

Auxiliary Space: O(1)

Bozo Sort Algorithm:

Bozo sort is a variation of Bogo sort and is little more efficient than Bogo sort.

Check if the array is sorted or not.
Unlike bogo sort, if the list/array is not sorted then it picks only two items at random and swap them.
Then it checks if the array/list is sorted or not.
But like bogo sort, there is chance that it faces the same pseudo-random problems and it may never terminate.
It means it also has O(∞) worst time complexity but its average case complexity is better than Bogo sort.

Question:

1. Tell the other names of Bogo sort?

Ans. Bogo sort has many other names like, permutation sort, slow sort, shotgun sort, stupid sort, bozo sort, blort sort, monkey sort, random sort or drunk man sort.

2. Why Bogo sort is called stupid sort, bozo sort, blort sort, monkey sort, random sort or drunk man sort?

Ans. Complexity of Bogo sort is O(∞) since this algorithm has no upper bound. So, you can imagine how much inefficient this sorting algorithm is. That’s why for its tremendous inefficiency, it is jokingly called stupid sort, bozo sort, blort sort, monkey sort, random sort or drunk man sort.

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