Bubble Sort Algorithm

Bubble Sort is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order. This algorithm is not suitable for large data sets as its average and worst-case time complexity is quite high.

How does Bubble Sort Work?

Input: arr[] = {5, 1, 4, 2, 8}

First Pass:

• Bubble sort starts with very first two elements, comparing them to check which one is greater.
  • ( 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:

• Now, during second iteration it should look like this:
  • ( 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 ) 

Third Pass:

• 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.
  • ( 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 ) 

Illustration:

Follow the below steps to solve the problem:

• Run a nested for loop to traverse the input array using two variables i and j, such that 0 ≤ i < n-1 and 0 ≤ j < n-i-1
• If arr[j] is greater than arr[j+1] then swap these adjacent elements, else move on
• Print the sorted array

Below is the implementation of the above approach:

C

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

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)
{
    int i, j;
    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]);
}

/* Function to print an array */
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        printf("%d ", arr[i]);
    printf("\n");
}

// Driver program to test above functions
int main()
{
    int arr[] = { 5, 1, 4, 2, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    bubbleSort(arr, n);
    printf("Sorted array: \n");
    printArray(arr, n);
    return 0;
}

C++

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

// A function to implement bubble sort
void bubbleSort(int arr[], int n)
{
    int i, j;
    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]);
}

// Function to print an array
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        cout << arr[i] << " ";
    cout << endl;
}

// Driver code
int main()
{
    int arr[] = { 5, 1, 4, 2, 8};
    int N = sizeof(arr) / sizeof(arr[0]);
    bubbleSort(arr, N);
    cout << "Sorted array: \n";
    printArray(arr, N);
    return 0;
}
// This code is contributed by rathbhupendra

Java

// Java program for implementation of Bubble Sort
import java.util.*;

class BubbleSort {
    void bubbleSort(int arr[])
    {
        int n = arr.length;
        for (int i = 0; i < n - 1; i++)
            for (int j = 0; j < n - i - 1; j++)
                if (arr[j] > arr[j + 1]) {
                    // swap arr[j+1] and arr[j]
                    int temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                }
    }

    /* Prints the array */
    void printArray(int arr[])
    {
        int n = arr.length;
        for (int i = 0; i < n; ++i)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver method to test above
    public static void main(String args[])
    {
        BubbleSort ob = new BubbleSort();
        int arr[] = { 5, 1, 4, 2, 8 };
        ob.bubbleSort(arr);
        System.out.println("Sorted array");
        ob.printArray(arr);
    }
}
/* This code is contributed by Rajat Mishra */

Python3

# Python program for implementation of Bubble Sort


def bubbleSort(arr):
    n = len(arr)

    # Traverse through all array elements
    for i in range(n):

        # Last i elements are already in place
        for j in range(0, n-i-1):

            # traverse the array from 0 to n-i-1
            # Swap if the element found is greater
            # than the next element
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]


# Driver code to test above
if __name__ == "__main__":
  arr = [5, 1, 4, 2, 8]

  bubbleSort(arr)

  print("Sorted array is:")
  for i in range(len(arr)):
      print("%d" % arr[i], end=" ")

C#

// C# program for implementation
// of Bubble Sort
using System;

class GFG {
    static void bubbleSort(int[] arr)
    {
        int n = arr.Length;
        for (int i = 0; i < n - 1; i++)
            for (int j = 0; j < n - i - 1; j++)
                if (arr[j] > arr[j + 1]) {
                    // swap temp and arr[i]
                    int temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                }
    }

    /* Prints the array */
    static void printArray(int[] arr)
    {
        int n = arr.Length;
        for (int i = 0; i < n; ++i)
            Console.Write(arr[i] + " ");
        Console.WriteLine();
    }

    // Driver method
    public static void Main()
    {
        int[] arr = { 5, 1, 4, 2, 8};
        bubbleSort(arr);
        Console.WriteLine("Sorted array");
        printArray(arr);
    }
}

// This code is contributed by Sam007

PHP

<?php
// PHP program for implementation
// of Bubble Sort

function bubbleSort(&$arr)
{
    $n = sizeof($arr);

    // Traverse through all array elements
    for($i = 0; $i < $n; $i++)
    {
        // Last i elements are already in place
        for ($j = 0; $j < $n - $i - 1; $j++)
        {
            // traverse the array from 0 to n-i-1
            // Swap if the element found is greater
            // than the next element
            if ($arr[$j] > $arr[$j+1])
            {
                $t = $arr[$j];
                $arr[$j] = $arr[$j+1];
                $arr[$j+1] = $t;
            }
        }
    }
}

// Driver code to test above
$arr = array(5, 1, 4, 2, 8);

$len = sizeof($arr);
bubbleSort($arr);

echo "Sorted array : \n";

for ($i = 0; $i < $len; $i++)
    echo $arr[$i]." ";

// This code is contributed by ChitraNayal.
?>

Javascript

<script>

function swap(arr, xp, yp)
{
    var temp = arr[xp];
    arr[xp] = arr[yp];
    arr[yp] = temp;
}

// An optimized version of Bubble Sort
function bubbleSort( arr, n)
{
var i, j;
for (i = 0; i < n-1; i++)
{
    for (j = 0; j < n-i-1; j++)
    {
        if (arr[j] > arr[j+1])
        {
        swap(arr,j,j+1);

        }
    }

}
}

/* Function to print an array */
function printArray(arr, size)
{
    var i;
    for (i=0; i < size; i++)
        document.write(arr[i]+ " ");
    document.write("\n");
}

// Driver program to test above functions
  var arr = [5, 1, 4, 2, 8];
    var n = 5;
    document.write("UnSorted array: \n");
    printArray(arr, n);

    bubbleSort(arr, n);
    document.write("Sorted array: \n");
    printArray(arr, n);


</script>

Output

Sorted array: 
1 2 4 5 8 

Time Complexity: O(N²)
Auxiliary Space: O(1) 

Optimized Implementation of Bubble Sort:

The above function always runs O(N²) time even if the array is sorted. It can be optimized by stopping the algorithm if the inner loop didn’t cause any swap. 

Below is the implementation for the above approach: 

C

// Optimized implementation of Bubble sort
#include <stdio.h>
#include <stdbool.h>

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

// An optimized version of Bubble Sort
void bubbleSort(int arr[], int n)
{
   int i, j;
   bool swapped;
   for (i = 0; i < n-1; i++)
   {
     swapped = false;
     for (j = 0; j < n-i-1; j++)
     {
        if (arr[j] > arr[j+1])
        {
           swap(&arr[j], &arr[j+1]);
           swapped = true;
        }
     }

     // IF no two elements were swapped by inner loop, then break
     if (swapped == false)
        break;
   }
}

/* Function to print an array */
void printArray(int arr[], int size)
{
    int i;
    for (i=0; i < size; i++)
        printf("%d ", arr[i]);
}

// 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;
}

C++

// Optimized implementation of Bubble sort
#include <bits/stdc++.h>
using namespace std;

// An optimized version of Bubble Sort
void bubbleSort(int arr[], int n)
{
   int i, j;
   bool swapped;
   for (i = 0; i < n-1; i++)
   {
     swapped = false;
     for (j = 0; j < n-i-1; j++)
     {
        if (arr[j] > arr[j+1])
        {
           swap(arr[j], arr[j+1]);
           swapped = true;
        }
     }

     // IF no two elements were swapped
     // by inner loop, then break
     if (swapped == false)
        break;
   }
}

// Function to print an array
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        cout <<" "<< arr[i];
}

// 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;
}
// This code is contributed by shivanisinghss2110

Java

// Optimized java implementation
// of Bubble sort
import java.io.*;

class GFG
{
    // An optimized version of Bubble Sort
    static void bubbleSort(int arr[], int n)
    {
        int i, j, temp;
        boolean swapped;
        for (i = 0; i < n - 1; i++)
        {
            swapped = false;
            for (j = 0; j < n - i - 1; j++)
            {
                if (arr[j] > arr[j + 1])
                {
                    // swap arr[j] and arr[j+1]
                    temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                    swapped = true;
                }
            }

            // IF no two elements were
            // swapped by inner loop, then break
            if (swapped == false)
                break;
        }
    }

    // Function to print an array
    static void printArray(int arr[], int size)
    {
        int i;
        for (i = 0; i < size; i++)
            System.out.print(arr[i] + " ");
        System.out.println();
    }

    // Driver program
    public static void main(String args[])
    {
        int arr[] = { 64, 34, 25, 12, 22, 11, 90 };
        int n = arr.length;
        bubbleSort(arr, n);
        System.out.println("Sorted array: ");
        printArray(arr, n);
    }
}


// This code is contributed
// by Nikita Tiwari.

Python3

# Optimized Python program for implementation of Bubble Sort

def bubbleSort(arr):
    n = len(arr)
    # Traverse through all array elements
    for i in range(n):
        swapped = False

        # Last i elements are already in place
        for j in range(0, n-i-1):

            # traverse the array from 0 to n-i-1
            # Swap if the element found is greater
            # than the next element
            if arr[j] > arr[j+1]:
                arr[j], arr[j+1] = arr[j+1], arr[j]
                swapped = True
        if (swapped == False):
            break


# Driver code to test above
if __name__ == "__main__":
    arr = [64, 34, 25, 12, 22, 11, 90]

    bubbleSort(arr)

    print("Sorted array is:")
    for i in range(len(arr)):
        print("%d" % arr[i], end=" ")

# This code is modified by Suraj krushna Yadav

C#

// Optimized C# implementation
// of Bubble sort
using System;

class GFG
{
    // An optimized version of Bubble Sort
    static void bubbleSort(int []arr, int n)
    {
        int i, j, temp;
        bool swapped;
        for (i = 0; i < n - 1; i++)
        {
            swapped = false;
            for (j = 0; j < n - i - 1; j++)
            {
                if (arr[j] > arr[j + 1])
                {
                    // swap arr[j] and arr[j+1]
                    temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                    swapped = true;
                }
            }

            // IF no two elements were
            // swapped by inner loop, then break
            if (swapped == false)
                break;
        }
    }

    // Function to print an array
    static void printArray(int []arr, int size)
    {
        int i;
        for (i = 0; i < size; i++)
            Console.Write(arr[i] + " ");
        Console.WriteLine();
    }

    // Driver method
    public static void Main()
    {
        int []arr = {64, 34, 25, 12, 22, 11, 90};
        int n = arr.Length;
        bubbleSort(arr,n);
        Console.WriteLine("Sorted array");
        printArray(arr,n);
    }

}
// This code is contributed by Sam007

PHP

<?php
// PHP Optimized implementation
// of Bubble sort

// An optimized version of Bubble Sort
function bubbleSort(&$arr)
{
    $n = sizeof($arr);

    // Traverse through all array elements
    for($i = 0; $i < $n; $i++)
    {
        $swapped = False;

        // Last i elements are already
        // in place
        for ($j = 0; $j < $n - $i - 1; $j++)
        {

            // traverse the array from 0 to
            // n-i-1. Swap if the element
            // found is greater than the
            // next element
            if ($arr[$j] > $arr[$j+1])
            {
                $t = $arr[$j];
                $arr[$j] = $arr[$j+1];
                $arr[$j+1] = $t;
                $swapped = True;
            }
        }

        // IF no two elements were swapped
        // by inner loop, then break
        if ($swapped == False)
            break;
    }
}

// Driver code to test above
$arr = array(64, 34, 25, 12, 22, 11, 90);
$len = sizeof($arr);
bubbleSort($arr);

echo "Sorted array : \n";

for($i = 0; $i < $len; $i++)
    echo $arr[$i]." ";

// This code is contributed by ChitraNayal.
?>

Javascript

<script>

// Optimized javaScript implementation
// of Bubble sort
// An optimized version of Bubble Sort
function bubbleSort(arr, n)
    {
        var i, j, temp;
        var swapped;
        for (i = 0; i < n - 1; i++)
        {
            swapped = false;
            for (j = 0; j < n - i - 1; j++)
            {
                if (arr[j] > arr[j + 1])
                {
                    // swap arr[j] and arr[j+1]
                    temp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = temp;
                    swapped = true;
                }
            }

            // IF no two elements were
            // swapped by inner loop, then break
            if (swapped == false)
                break;
        }
    }

    // Function to print an array
    function printArray(arr, size)
    {
        var i;
        for (i = 0; i < size; i++)
            document.write(arr[i] + " ");
        document.writeln();
    }

    // Driver program
        var arr = [ 64, 34, 25, 12, 22, 11, 90 ];
        var n = arr.length;
        bubbleSort(arr, n);
        document.write("Sorted array: ");
        printArray(arr, n);

// This code is contributed shivanisinghss2110
</script>

Output

Sorted array: 
11 12 22 25 34 64 90 

Time Complexity: O(N²)
Auxiliary Space: O(1)

Worst Case Analysis for Bubble Sort:

The worst-case condition for bubble sort occurs when elements of the array are arranged in decreasing order.
In the worst case, the total number of iterations or passes required to sort a given array is (n-1). where ‘n’ is a number of elements present in the array.

At pass 1 :  Number of comparisons = (n-1)
                     Number of swaps = (n-1)

At pass 2 :  Number of comparisons = (n-2)
                     Number of swaps = (n-2)

At pass 3 :  Number of comparisons = (n-3)
                    Number of swaps = (n-3)
.
                             .
                             .
At pass n-1 :  Number of comparisons = 1
                        Number of swaps = 1

Now , calculating total number of comparison required to sort the array
= (n-1) + (n-2) +  (n-3) + . . . 2 + 1
= (n-1)*(n-1+1)/2  { by using sum of N natural Number formula }
= n (n-1)/2 

For the Worst case:

Total number of swaps = Total number of comparison
Total number of comparison (Worst case) = n(n-1)/2
Total number of swaps (Worst case) = n(n-1)/2

Worst and Average Case Time Complexity: O(N²). The worst case occurs when an array is reverse sorted.
Best Case Time Complexity: O(N). The best case occurs when an array is already sorted.
Auxiliary Space: O(1)

Recursive Implementation Of Bubble Sort:

The idea is to place the largest element in its position and keep doing the same for every other element.

Algorithm:

1. Start with an array of unsorted numbers
2. Define a function called “bubbleSort” that takes in the array and the length of the array as parameters
3. In the function, create a variable called “sorted” that is set to true
4. Create a for loop that iterates through the array starting at index 0 and ending at the length of the array -1
5. Within the for loop, compare the current element with the next element in the array
6. If the current element is greater than the next element, swap their positions and set “sorted” to false
7. After the for loop, check if “sorted” is false
8. If “sorted” is false, call the “bubbleSort” function again with the same array and length as parameters
9. If “sorted” is true, the array is now sorted and the function will return the sorted array
10. Call the “bubbleSort” function with the initial unsorted array and its length as parameters to begin the sorting process.

Below is the implementation of the above approach:

C

#include "stdbool.h"
#include <stdio.h>

void bubbleSort(int a[], int n)
{
    bool sorted = true;
    // we are assuming that array is sorted

    for (int i = 0; i < n - 1; i++) {
        if (a[i] > a[i + 1]) {
            int t = a[i];
            a[i] = a[i + 1];
            a[i + 1] = t;

            sorted = false;
            // now array is not sorted
        }
        // if there are no swaps then we can
        // say that array is sorted.
    }
    if (sorted == false) {
        // recursively calling until it was sorted.
        bubbleSort(a, n);
    }
}

int main()
{

    int ar[] = { 5, 4, 8, 2, 9, 7, 3 };
    int n = sizeof(ar) / sizeof(int);
    bubbleSort(ar, n);

    printf("Sorted array : ");
    for (int i = 0; i < n; i++) {
        printf("%d ", ar[i]);
    }
    printf("\n");

    return 0;
}

// This code was contributed by aeroabrar_31

C++

#include <bits/stdc++.h>
#include <iostream>
using namespace std;

void bubbleSort(int a[], int n)
{
    bool sorted = true;
    //we are assuming that array is sorted

    for (int i = 0; i < n - 1; i++) {
        if (a[i] > a[i + 1]) {
            int t = a[i];
            a[i] = a[i + 1];
            a[i + 1] = t;

            sorted = false;
          //now array is not sorted
        }
        //if there are no swaps then we can
        //say that array is sorted.
    }
    if (sorted == false)
    {
          //recursively calling until it was sorted.
        bubbleSort(a, n);
    }
}

int main()
{

    int ar[] = { 5, 4, 8, 2, 9, 7, 3 };
    int n = sizeof(ar) / sizeof(int);
    bubbleSort(ar, n);

    cout << "Sorted array : ";
    for (int i = 0; i < n; i++) {
        cout << ar[i] << " ";
    }
    cout << endl;

    return 0;
}
// This code was contributed by aeroabrar_31

Java

/*package whatever //do not write package name here */

import java.util.*;
class GFG
{
    public static void main(String[] args) {

        int[] ar={5,4,8,2,9,7,3};
        bubbleSort(ar,ar.length);

        System.out.print("Sorted array : ");
        for(int ele:ar)
        {
            System.out.print(ele+" ");
        }
        System.out.println();

    }
    public static void bubbleSort(int[] a,int n)
    {
        boolean sorted=true;
      //we are assuming that array is sorted

        for(int i=0;i<n-1;i++)
        {
            if(a[i]>a[i+1])
            {
                int t=a[i];
                a[i]=a[i+1];
                a[i+1]=t;

                sorted=false;
              //now array is not sorted
            }
          //if there are no swaps then we can
          //say that array is sorted.

        }
        if(sorted==false)
        {
            //recursively calling until it was sorted.
            bubbleSort(a,n);
        }
    }
}
// This code is contributed by aeroabrar_31

Python3

def bubbleSort(a, n):

    sorted = True
    # we are assuming that array is sorted
    for i in range(0, n-1):
        if a[i] > a[i+1]:
            #swap
            a[i], a[i+1] = a[i+1], a[i]
            sorted = False
            # now array is not sorted

        # if there are no swaps then we can
        # say that array is sorted.

    if sorted == False:
        #recursively calling until it was sorted.
        bubbleSort(arr, n)


# Driver code to test above
if __name__ == "__main__":
    arr = [5, 4, 8, 2, 9, 7, 3]
    n = len(arr)
    bubbleSort(arr, n)

    print("Sorted array : ", end=" ")
    for i in range(len(arr)):
        print("%d" % arr[i], end=" ")

# This code is contributed by aeroabrar_31

Javascript

function bubbleSort(a, n) {
    let sorted = true; // we are assuming that array is sorted
    for (let i = 0; i < n - 1; i++) {
        if (a[i] > a[i + 1]) {
            let t = a[i];
            a[i] = a[i + 1];
            a[i + 1] = t;
            sorted = false; // now array is not sorted
        }
        // if there are no swaps then we can say that array is sorted.
    }
    if (sorted == false) {
        // recursively calling until it was sorted.
        bubbleSort(a, n);
    }
}

let ar = [5, 4, 8, 2, 9, 7, 3];
let n = ar.length;
bubbleSort(ar, n);

console.log("Sorted array : " + ar.join(" "));

Output

Sorted array : 2 3 4 5 7 8 9 

Time Complexity : O (N² )

Auxiliary space : O(1)

What is the Boundary Case for Bubble sort?

Bubble sort takes minimum time (Order of n) when elements are already sorted. Hence it is best to check if the array is already sorted or not beforehand, to avoid O(N²) time complexity.

Does sorting happen in place in Bubble sort?

Yes, Bubble sort performs the swapping of adjacent pairs without the use of any major data structure. Hence Bubble sort algorithm is an in-place algorithm.

Is the Bubble sort algorithm stable?

Yes, the bubble sort algorithm is stable.

Where is the Bubble sort algorithm used?

Due to its simplicity, bubble sort is often used to introduce the concept of a sorting algorithm. 
In computer graphics, it is popular for its capability to detect a tiny error (like a swap of just two elements) in almost-sorted arrays and fix it with just linear 
complexity (2n). 

Example: It is used in a polygon filling algorithm, where bounding lines are sorted by their x coordinate at a specific scan line (a line parallel to the x-axis), and with incrementing y their order changes (two elements are swapped) only at intersections of two lines (Source: Wikipedia)

Advantages:

• Bubble sort is easy to understand and implement.
• It does not require any additional memory space.
• It’s adaptability to different types of data.
• It is a stable sorting algorithm, meaning that elements with the same key value maintain their relative order in the sorted output.

Disadvantages

• Bubble sort has a time complexity of O(n^2) which makes it very slow for large data sets.
• It is not efficient for large data sets, because it requires multiple passes through the data.

Snapshots: Quiz on Bubble Sort

Other Sorting Algorithms on GeeksforGeeks/GeeksQuiz:
Recursive Bubble Sort
Coding practice for sorting.