Recursive Bubble Sort

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.  

1. Base Case: If array size is 1, return.
2. Do One Pass of normal Bubble Sort. This pass fixes last element of current subarray.
3. Recur for all elements except last of current subarray.

Below is implementation of above idea.

// C++ program for recursive implementation
// of Bubble sort
#include <bits/stdc++.h>
using namespace std;

// A function to implement bubble sort
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]);
            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++)
        cout<<arr[i]<<" ";
    cout<<"\n";
}

// Driver program to test above functions
int main()
{
    int arr[] = {64, 34, 25, 12, 22, 11, 90};
    int n = sizeof(arr)/sizeof(arr[0]);
    bubbleSort(arr, n);
    cout<<"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 sort
class 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 Code
def 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 sort
using System;

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++;
        }

      // 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
static 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>

// C program for recursive implementation
// of Bubble sort
#include <stdio.h>

// Swap function
void swap(int *xp, int *yp)
{
    int temp = *xp;
    *xp = *yp;
    *yp = temp;
}

// A function to implement bubble sort
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]);
            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 functions
int 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;
}

// This code is submitted by Susobhan Akhuli

<?php
// PHP program for recursive implementation of Bubble sort
  
// A function to implement bubble sort
function bubbleSort(&$arr, $n)
{
    // Base case
    if ($n == 1)
        return;

    $count = 0;
    // One pass of bubble sort. After
    // this pass, the largest element
    // is moved (or bubbled) to end.
    for ($i=0; $i<$n-1; $i++)
        if ($arr[$i] > $arr[$i+1]){
              list($arr[$i], $arr[$i+1]) = array($arr[$i+1], $arr[$i]);
            $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 */
function printArray($arr, $n)
{
    for ($i=0; $i < $n; $i++)
        echo $arr[$i]." ";
    echo "\n";
}

// Driver program to test above functions
$arr = array(64, 34, 25, 12, 22, 11, 90);
$n = sizeof($arr);
bubbleSort($arr, $n);
echo "Sorted array : \n";
printArray($arr, $n);

// This code is submitted by Susobhan Akhuli
?>

Sorted array : 
11 12 22 25 34 64 90 

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

Question:

1. Difference between iterative and recursive bubble sort?
Ans. Recursive bubble sort runs on O(n) auxiliary space complexity whereas iterative bubble sort runs on O(1) auxiliary space complexity.

2. Which is faster iterative or recursive bubble sort?
Ans. Based on the number of comparisons in each method, the recursive bubble sort is better than the iterative bubble sort, but the time complexity for both the methods is same.

3. Which sorting method we should prefer more iterative or recursive bubble sort?
Ans. Both the methods complete the computation at the same time(according to time complexity analysis) but iterative code takes less memory than recursive one, so we should prefer iterative bubble sort more than recursive bubble sort.