Bubble Sort - GeeksforGeeks

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 )

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Following is the implementations of Bubble Sort.

C++

// C++ program for implementation of Bubble sort  
#include <bits/stdc++.h> 
using namespace std; 
  
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++)  
        cout << arr[i] << " ";  
    cout << endl;  
}  
  
// Driver code  
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 rathbhupendra 

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[] = {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 implementation of Bubble Sort 
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[i] 
                    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[] = {64, 34, 25, 12, 22, 11, 90}; 
        ob.bubbleSort(arr); 
        System.out.println("Sorted array"); 
        ob.printArray(arr); 
    } 
} 
/* This code is contributed by Rajat Mishra */

Python

# 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 
arr = [64, 34, 25, 12, 22, 11, 90] 
  
bubbleSort(arr) 
  
print ("Sorted array is:") 
for i in range(len(arr)): 
    print ("%d" %arr[i]),  

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 = {64, 34, 25, 12, 22, 11, 90}; 
        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(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. 
?> 

Output:

Sorted array:
11 12 22 25 34 64 90

<!—-Illustration :
—>

Optimized Implementation:
The above function always runs O(n^2) time even if the array is sorted. It can be optimized by stopping the algorithm if inner loop didn’t cause any swap.

CPP

// Optimized implementation of Bubble sort 
#include <stdio.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]); 
    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; 
} 

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

# Python3 Optimized implementation 
# of Bubble sort 
  
# An optimized version 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 no two elements were swapped 
        # by inner loop, then break 
        if swapped == False: 
            break
           
# Driver code to test above 
arr = [64, 34, 25, 12, 22, 11, 90] 
   
bubbleSort(arr) 
   
print ("Sorted array :") 
for i in range(len(arr)): 
    print ("%d" %arr[i],end=" ") 
  
# This code is contributed by Shreyanshi Arun 

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. 
?> 

Output:

Sorted array:
11 12 22 25 34 64 90

Worst and Average Case Time Complexity: O(n*n). Worst case occurs when array is reverse sorted.

Best Case Time Complexity: O(n). Best case occurs when array is already sorted.

Auxiliary Space: O(1)

Boundary Cases: Bubble sort takes minimum time (Order of n) when elements are already sorted.

Sorting In Place: Yes

Stable: Yes

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 very small error (like swap of just two elements) in almost-sorted arrays and fix it with just linear complexity (2n). For 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 x axis) and with incrementing y their order changes (two elements are swapped) only at intersections of two lines (Source: Wikipedia)