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 swapping occur or not   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 

// 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 swapping occur or not   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 

// 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 swapping occur or not   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 swapping occur or not  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 swapping occur or not   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 

// JavaScript program for recursive implementation of Bubble Sort using console.log function bubbleSort(arr, n) {  // Base case  if (n == 1)  return;  let count = 0;  // One pass of bubble sort  for (let i = 0; i < n - 1; i++) {  if (arr[i] > arr[i + 1]) {  // Swap arr[i] and arr[i+1]  let temp = arr[i];  arr[i] = arr[i + 1];  arr[i + 1] = temp;  count++;  }  }  // If no elements were swapped, the array is sorted  if (count == 0)  return;  // Recursive call for remaining array  bubbleSort(arr, n - 1); } // Driver code let arr = [64, 34, 25, 12, 22, 11, 90]; bubbleSort(arr, arr.length); console.log("Sorted array:"); console.log(arr.join(" ")); 

<?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]); $count++; } //check if any swapping occur or not  if ($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.