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Bubble Sort

In this tutorial, you will learn about the bubble sort algorithm and its implementation in Python, Java, C, and C++.

Bubble sort is a sorting algorithm that compares two adjacent elements and swaps them until they are not in the intended order.

Just like the movement of air bubbles in the water that rise up to the surface, each element of the array move to the end in each iteration. Therefore, it is called a bubble sort.


Working of Bubble Sort

Suppose we are trying to sort the elements in ascending order.

1. First Iteration (Compare and Swap)

  1. Starting from the first index, compare the first and the second elements.
  2. If the first element is greater than the second element, they are swapped.
  3. Now, compare the second and the third elements. Swap them if they are not in order.
  4. The above process goes on until the last element.
    Compare two adjacent elements and swap them if the first element is greater than the next element
    Compare the Adjacent Elements

2. Remaining Iteration

The same process goes on for the remaining iterations.

After each iteration, the largest element among the unsorted elements is placed at the end.

Continue the swapping and put the largest element among the unsorted list at the end
Put the largest element at the end

In each iteration, the comparison takes place up to the last unsorted element.

Swapping occurs only if the first element is greater than the next element
Compare the adjacent elements

The array is sorted when all the unsorted elements are placed at their correct positions.

The array is sorted if all the elements are kept in the right order.
The array is sorted if all elements are kept in the right order

Bubble Sort Algorithm

bubbleSort(array)
  for i <- 1 to indexOfLastUnsortedElement-1
    if leftElement > rightElement
      swap leftElement and rightElement
end bubbleSort

Bubble Sort Code in Python, Java and C/C++

# Bubble sort in Python

def bubbleSort(array):
    
  # loop to access each array element
  for i in range(len(array)):

    # loop to compare array elements
    for j in range(0, len(array) - i - 1):

      # compare two adjacent elements
      # change > to < to sort in descending order
      if array[j] > array[j + 1]:

        # swapping elements if elements
        # are not in the intended order
        temp = array[j]
        array[j] = array[j+1]
        array[j+1] = temp


data = [-2, 45, 0, 11, -9]

bubbleSort(data)

print('Sorted Array in Ascending Order:')
print(data)
// Bubble sort in Java

import java.util.Arrays;

class Main {

  // perform the bubble sort
  static void bubbleSort(int array[]) {
    int size = array.length;
    
    // loop to access each array element
    for (int i = 0; i < size - 1; i++)
    
      // loop to compare array elements
      for (int j = 0; j < size - i - 1; j++)

        // compare two adjacent elements
        // change > to < to sort in descending order
        if (array[j] > array[j + 1]) {

          // swapping occurs if elements
          // are not in the intended order
          int temp = array[j];
          array[j] = array[j + 1];
          array[j + 1] = temp;
        }
  }

  public static void main(String args[]) {
      
    int[] data = { -2, 45, 0, 11, -9 };
    
    // call method using class name
    Main.bubbleSort(data);
    
    System.out.println("Sorted Array in Ascending Order:");
    System.out.println(Arrays.toString(data));
  }
}
// Bubble sort in C

#include <stdio.h>

// perform the bubble sort
void bubbleSort(int array[], int size) {

  // loop to access each array element
  for (int step = 0; step < size - 1; ++step) {
      
    // loop to compare array elements
    for (int i = 0; i < size - step - 1; ++i) {
      
      // compare two adjacent elements
      // change > to < to sort in descending order
      if (array[i] > array[i + 1]) {
        
        // swapping occurs if elements
        // are not in the intended order
        int temp = array[i];
        array[i] = array[i + 1];
        array[i + 1] = temp;
      }
    }
  }
}

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

int main() {
  int data[] = {-2, 45, 0, 11, -9};
  
  // find the array's length
  int size = sizeof(data) / sizeof(data[0]);

  bubbleSort(data, size);
  
  printf("Sorted Array in Ascending Order:\n");
  printArray(data, size);
}
// Bubble sort in C++

#include <iostream>
using namespace std;

// perform bubble sort
void bubbleSort(int array[], int size) {

  // loop to access each array element
  for (int step = 0; step < (size-1); ++step) {
      
    // loop to compare array elements
    for (int i = 0; i < size - (step-1); ++i) {

      // compare two adjacent elements
      // change > to < to sort in descending order
      if (array[i] > array[i + 1]) {

        // swapping elements if elements
        // are not in the intended order
        int temp = array[i];
        array[i] = array[i + 1];
        array[i + 1] = temp;
      }
    }
  }
}

// print array
void printArray(int array[], int size) {
  for (int i = 0; i < size; ++i) {
    cout << "  " << array[i];
  }
  cout << "\n";
}

int main() {
  int data[] = {-2, 45, 0, 11, -9};
  
  // find array's length
  int size = sizeof(data) / sizeof(data[0]);
  
  bubbleSort(data, size);
  
  cout << "Sorted Array in Ascending Order:\n";  
  printArray(data, size);
}

Optimized Bubble Sort Algorithm

In the above algorithm, all the comparisons are made even if the array is already sorted.

This increases the execution time.

To solve this, we can introduce an extra variable swapped. The value of swapped is set true if there occurs swapping of elements. Otherwise, it is set false.

After an iteration, if there is no swapping, the value of swapped will be false. This means elements are already sorted and there is no need to perform further iterations.

This will reduce the execution time and helps to optimize the bubble sort.

Algorithm for optimized bubble sort is

bubbleSort(array)
  swapped <- false
  for i <- 1 to indexOfLastUnsortedElement-1
    if leftElement > rightElement
      swap leftElement and rightElement
      swapped <- true
end bubbleSort

Optimized Bubble Sort in Python, Java, and C/C++

# Optimized Bubble sort in Python

def bubbleSort(array):
    
  # loop through each element of array
  for i in range(len(array)):
        
    # keep track of swapping
    swapped = False
    
    # loop to compare array elements
    for j in range(0, len(array) - i - 1):

      # compare two adjacent elements
      # change > to < to sort in descending order
      if array[j] > array[j + 1]:

        # swapping occurs if elements
        # are not in the intended order
        temp = array[j]
        array[j] = array[j+1]
        array[j+1] = temp

        swapped = True
          
    # no swapping means the array is already sorted
    # so no need for further comparison
    if not swapped:
      break

data = [-2, 45, 0, 11, -9]

bubbleSort(data)

print('Sorted Array in Ascending Order:')
print(data)
// Optimized Bubble sort in Java

import java.util.Arrays;

class Main {

  // perform the bubble sort
  static void bubbleSort(int array[]) {
    int size = array.length;
    
    // loop to access each array element
    for (int i = 0; i < (size-1); i++) {
    
      // check if swapping occurs
      boolean swapped = false;
      
      // loop to compare adjacent elements
      for (int j = 0; j < (size-i-1); j++) {

        // compare two array elements
        // change > to < to sort in descending order
        if (array[j] > array[j + 1]) {

          // swapping occurs if elements
          // are not in the intended order
          int temp = array[j];
          array[j] = array[j + 1];
          array[j + 1] = temp;
          
          swapped = true;
        }
      }
      // no swapping means the array is already sorted
      // so no need for further comparison
      if (!swapped)
        break;

    }
  }

  public static void main(String args[]) {
      
    int[] data = { -2, 45, 0, 11, -9 };
    
    // call method using the class name
    Main.bubbleSort(data);
    
    System.out.println("Sorted Array in Ascending Order:");
    System.out.println(Arrays.toString(data));
  }
}
// Optimized Bubble sort in C

#include 

// perform the bubble sort
void bubbleSort(int array[], int size) {

  // loop to access each array element
  for (int step = 0; step < size - 1; ++step) {
    
    // check if swapping occurs  
    int swapped = 0;
    
    // loop to compare array elements
    for (int i = 0; i < size - step - 1; ++i) {
      
      // compare two array elements
      // change > to < to sort in descending order
      if (array[i] > array[i + 1]) {
        
        // swapping occurs if elements
        // are not in the intended order
        int temp = array[i];
        array[i] = array[i + 1];
        array[i + 1] = temp;
        
        swapped = 1;
      }
    }
    
    // no swapping means the array is already sorted
    // so no need for further comparison
    if (swapped == 0) {
      break;
    }
    
  }
}

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

// main method
int main() {
  int data[] = {-2, 45, 0, 11, -9};
  
  // find the array's length
  int size = sizeof(data) / sizeof(data[0]);

  bubbleSort(data, size);
  
  printf("Sorted Array in Ascending Order:\n");
  printArray(data, size);
}
// Optimized bubble sort in C++

#include 
using namespace std;

// perform bubble sort
void bubbleSort(int array[], int size) {
    
  // loop to access each array element
  for (int step = 0; step < (size-1); ++step) {
      
    // check if swapping occurs
    int swapped = 0;
    
    // loop to compare two elements
    for (int i = 0; i < (size-step-1); ++i) {
        
      // compare two array elements
      // change > to < to sort in descending order
      if (array[i] > array[i + 1]) {

        // swapping occurs if elements
        // are not in intended order 
        int temp = array[i];
        array[i] = array[i + 1];
        array[i + 1] = temp;
        
        swapped = 1;
      }
    }

    // no swapping means the array is already sorted
    // so no need of further comparison
    if (swapped == 0)
      break;
  }
}

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

int main() {
  int data[] = {-2, 45, 0, 11, -9};
  
  // find the array's length
  int size = sizeof(data) / sizeof(data[0]);
  
  bubbleSort(data, size);
  
  cout << "Sorted Array in Ascending Order:\n";
  printArray(data, size);
}

Bubble Sort Complexity

Time Complexity  
Best O(n)
Worst O(n2)
Average O(n2)
Space Complexity O(1)
Stability Yes

Complexity in Detail

Bubble Sort compares the adjacent elements.

Cycle Number of Comparisons
1st (n-1)
2nd (n-2)
3rd (n-3)
....... ......
last 1

Hence, the number of comparisons is

(n-1) + (n-2) + (n-3) +.....+ 1 = n(n-1)/2

nearly equals to n2

Hence, Complexity: O(n2)

Also, if we observe the code, bubble sort requires two loops. Hence, the complexity is n*n = n2

1. Time Complexities

  • Worst Case Complexity: O(n2)
    If we want to sort in ascending order and the array is in descending order then the worst case occurs.
  • Best Case Complexity: O(n)
    If the array is already sorted, then there is no need for sorting.
  • Average Case Complexity: O(n2)
    It occurs when the elements of the array are in jumbled order (neither ascending nor descending).

2. Space Complexity

  • Space complexity is O(1) because an extra variable is used for swapping.
  • In the optimized bubble sort algorithm, two extra variables are used. Hence, the space complexity will be O(2).

Bubble Sort Applications

Bubble sort is used if

  • complexity does not matter
  • short and simple code is preferred

Similar Sorting Algorithms

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