Recursive Bubble Sort

20 Jun, 2022
Background : Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in wrong order.Example: First Pass: ( 5 1 4 2 8 ) –> ( 1 5 4 2 8 ), Here, algorithm compares the first two elements, and swaps since 5 > 1. ( 1 5 4 2 8 ) –> ( 1 4 5 2 8 ), Swap since 5 > 4 ( 1 4 5 2 8 ) –> ( 1 4 2 5 8 ), Swap since 5 > 2 ( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ), Now, since these elements are already in order (8 > 5), algorithm does not swap them.Second Pass: ( 1 4 2 5 8 ) –> ( 1 4 2 5 8 ) ( 1 4 2 5 8 ) –> ( 1 2 4 5 8 ), Swap since 4 > 2 ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) Now, the array is already sorted, but our algorithm does not know if it is completed. The algorithm needs one whole pass without any swap to know it is sorted.Third Pass: ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 ) ( 1 2 4 5 8 ) –> ( 1 2 4 5 8 )Following is iterative Bubble sort algorithm : 
// Iterative Bubble Sort
bubbleSort(arr[], n)
{
  for (i = 0; i < n-1; i++)      

     // Last i elements are already in place   
     for (j = 0; j < n-i-1; j++)
     {
         if(arr[j] > arr[j+1])
             swap(arr[j], arr[j+1]);
     }
} 
See Bubble Sort for more details.How to implement it recursively? Recursive Bubble Sort has no performance/implementation advantages, but can be a good question to check one’s understanding of Bubble Sort and recursion.If we take a closer look at Bubble Sort algorithm, we can notice that in first pass, we move largest element to end (Assuming sorting in increasing order). In second pass, we move second largest element to second last position and so on. Recursion Idea.  
Base Case: If array size is 1, return.Do One Pass of normal Bubble Sort. This pass fixes last element of current subarray.Recur for all elements except last of current subarray.
Base Case: If array size is 1, return.
Do One Pass of normal Bubble Sort. This pass fixes last element of current subarray.
Recur for all elements except last of current subarray.
Below is implementation of above idea.
C++
Java
Python3
C#
Javascript
// C/C++ program for recursive implementation// of Bubble sort#include <bits/stdc++.h>using namespace std;  // A function to implement bubble sortvoid bubbleSort(int arr[], int n){    // Base case    if (n == 1)        return;      int count = 0;    // One pass of bubble sort. After    // this pass, the largest element    // is moved (or bubbled) to end.    for (int i=0; i<n-1; i++)        if (arr[i] > arr[i+1]){            swap(arr[i], arr[i+1]);            count++;        }        // Check if any recursion happens or not      // If any recursion is not happen then return      if (count==0)           return;      // Largest element is fixed,    // recur for remaining array    bubbleSort(arr, n-1);}  /* Function to print an array */void printArray(int arr[], int n){    for (int i=0; i < n; i++)        printf("%d ", arr[i]);    printf("\n");}  // Driver program to test above functionsint main(){    int arr[] = {64, 34, 25, 12, 22, 11, 90};    int n = sizeof(arr)/sizeof(arr[0]);    bubbleSort(arr, n);    printf("Sorted array : \n");    printArray(arr, n);    return 0;}  // Code improved by Susobhan AKhuli
// Java program for recursive implementation// of Bubble sort  import java.util.Arrays;  public class GFG {    // A function to implement bubble sort    static void bubbleSort(int arr[], int n)    {        // Base case        if (n == 1)            return;           int count = 0;        // One pass of bubble sort. After        // this pass, the largest element        // is moved (or bubbled) to end.        for (int i=0; i<n-1; i++)            if (arr[i] > arr[i+1])            {                // swap arr[i], arr[i+1]                int temp = arr[i];                arr[i] = arr[i+1];                arr[i+1] = temp;                  count = count+1;            }            // Check if any recursion happens or not          // If any recursion is not happen then return         if (count == 0)            return;          // Largest element is fixed,        // recur for remaining array        bubbleSort(arr, n-1);    }          // Driver Method    public static void main(String[] args)    {        int arr[] = {64, 34, 25, 12, 22, 11, 90};               bubbleSort(arr, arr.length);                  System.out.println("Sorted array : ");        System.out.println(Arrays.toString(arr));    }}  // Code improved by Susobhan AKhuli
# Python Program for implementation of# Recursive Bubble sortclass bubbleSort:    """     bubbleSort:          function:              bubbleSortRecursive : recursive                   function to sort array              __str__ : format print of array              __init__ : constructor                   function in python          variables:              self.array = contains array              self.length = length of array    """      def __init__(self, array):        self.array = array        self.length = len(array)      def __str__(self):        return " ".join([str(x)                         for x in self.array])      def bubbleSortRecursive(self, n=None):        if n is None:            n = self.length        count = 0          # Base case        if n == 1:            return        # One pass of bubble sort. After        # this pass, the largest element        # is moved (or bubbled) to end.        for i in range(n - 1):            if self.array[i] > self.array[i + 1]:                self.array[i], self.array[i +                1] = self.array[i + 1], self.array[i]                count = count + 1          # Check if any recursion happens or not          # If any recursion is not happen then return        if (count==0):            return          # Largest element is fixed,        #  recur for remaining array        self.bubbleSortRecursive(n - 1)  # Driver Codedef main():    array = [64, 34, 25, 12, 22, 11, 90]          # Creating object for class    sort = bubbleSort(array)          # Sorting array    sort.bubbleSortRecursive()    print("Sorted array :\n", sort)    if __name__ == "__main__":    main()  # Code contributed by Mohit Gupta_OMG, # improved by itsvinayak# Code improved by Susobhan AKhuli
// C# program for recursive // implementation of Bubble sortusing System;  class GFG{  // A function to implement// bubble sortstatic void bubbleSort(int []arr,                          int n){    // Base case    if (n == 1)        return;       int count = 0;    // One pass of bubble     // sort. After this pass,    // the largest element    // is moved (or bubbled)     // to end.    for (int i = 0; i < n - 1; i++)        if (arr[i] > arr[i + 1])        {            // swap arr[i], arr[i+1]            int temp = arr[i];            arr[i] = arr[i + 1];            arr[i + 1] = temp;            count++;        }        // Check if any recursion happens or not      // If any recursion is not happen then return      if (count==0)           return;      // Largest element is fixed,    // recur for remaining array    bubbleSort(arr, n - 1);}  // Driver codestatic void Main(){    int []arr = {64, 34, 25,                  12, 22, 11, 90};      bubbleSort(arr, arr.Length);          Console.WriteLine("Sorted array : ");    for(int i = 0; i < arr.Length; i++)    Console.Write(arr[i] + " ");}}  // This code is contributed // by Sam007  // Code improved by Susobhan AKhuli
<script>// javascript program for recursive// implementation of Bubble sort  // A function to implement// bubble sort  function bubbleSort(arr, n){      // Base case    if (n == 1)        return;      var count = 0;    // One pass of bubble    // sort. After this pass,    // the largest element    // is moved (or bubbled)    // to end.          for (var i = 0; i < n - 1; i++)        if (arr[i] > arr[i + 1])        {                      // swap arr[i], arr[i+1]            var temp = arr[i];            arr[i] = arr[i + 1];            arr[i + 1] = temp;            count++;        }      // Check if any recursion happens or not      // If any recursion is not happen then return    if (count == 0)        return;      // Largest element is fixed,    // recur for remaining array    bubbleSort(arr, n - 1);}   // Driver code      var arr = [64, 34, 25, 12, 22, 11, 90 ]    bubbleSort(arr, arr.length);    document.write("Sorted array : " + "<br>");    for(var i = 0; i < arr.length; i++) {    document.write(arr[i] + " ");    }          // This code is contributed by bunnyram19.    // Code improved by Susobhan AKhuli    </script>
Sorted array : 
11 12 22 25 34 64 90 

Time Complexity: O(n*n)
Auxiliary Space: O(n)
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