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 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.
Below is implementation of above idea.
C++
// 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; // 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]); // 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;} |
Java
// Java program for recursive implementation// of Bubble sortimport 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; // 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; } // 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)); }} |
Python3
# 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 # 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] # 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 |
C#
// 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; // 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; } // 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 |
Output :
Sorted array : 11 12 22 25 34 64 90
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