# 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++

 `// C++ program for recursive implementation ` `// of Bubble sort ` `#include ` `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 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<

## Java

 `// 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 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`

## Python3

 `# 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#

 `// 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 `

## Javascript

 ``

## C

 `// C program for recursive implementation ` `// of Bubble sort ` `#include ` ` `  `// 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 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

 ` ``\$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 ` `?> `

Output

```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.

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