Bubble Sort

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 the implementations of Bubble Sort.

C/C++

 // C program for implementation of Bubble sort #include    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);     bubbleSort(arr, n);     printf("Sorted array: ");     printArray(arr, n);     return 0; }

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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

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

 \$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 : ";    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

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    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);     bubbleSort(arr, n);     printf("Sorted array: ");     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

 \$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 : ";    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)