Bubble sort is a sorting algorithm that compares two adjacent elements and swaps them until they are 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 Java

      
      
        // 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));
          }
        }

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 Java

            
// Optimized Bubble sort in Java import java.util.Arrays; class Main { // perform the bubble sort 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)); } }

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