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Cuneyt Yildirim | Nov 16, 2025 min read

Recursive Bubble Sort

Posted 2025-11-16 | *By : Cuneyt Yildirim *# Recursive Bubble Sort

Bubble Sort is one of the simplest sorting algorithms that compares two elements at a time and swaps them if they are in the wrong order. This process is repeated until the entire sequence is in order.

  • Time Complexity: O(n ^ 2) for average case; O(n) for best case.
  • Space Complexity: O(n); note that iterative bubble sort has space complexity as O(1).

Steps

Base case: If the size of the array is 1, return.

  • We need to fix the last element of the current sub-array. For this, iterate over the entire array using normal Bubble Sort, and perform swapping.
  • Next, call the function on the entire array excluding the last element(which was fixed by the iteration in the above step)
  • Repeat until Base Case is reached.

Example

Let the given array be: {5, 3, 2, 1, 4}

First Iteration:

  • {5, 3, 2, 1, 4} -> {3, 5, 2, 1, 4} Swap since 5 > 3
  • {3, 5, 2, 1, 4} -> {3, 2, 5, 1, 4} Swap since 5 > 2
  • {3, 2, 5, 1, 4} -> {3, 2, 1, 5, 4} Swap since 5 > 1
  • {3, 2, 1, 5, 4} -> {3, 2, 1, 4, 5} Swap since 5 > 4

This iteration has fixed the position of 5. Now, we will consider the array up to index 3.

Second Iteration:

  • {3, 2, 1, 4, 5} -> {2, 3, 1, 4, 5} Swap since 3 > 2
  • {2, 3, 1, 4, 5} -> {2, 1, 3, 4, 5} Swap since 3 > 1
  • {2, 1, 3, 4, 5}; As 3 < 4, do not swap

Note: As we check one less element with every iteration, we do not need elements at index 3 and 4 i.e., 4 and 5, as 5 is already in order. Formally, for an array with n integers, we consider elements only up to index n - i, where i is the iteration number.

Third Iteration:

  • {2, 1, 3, 4, 5} -> {1, 2, 3, 4, 5} Swap since 1 > 2
  • {1, 2, 3, 4, 5}; As 2 < 3, do not swap

Fourth Iteration:

  • {1, 2, 3, 4, 5}; As 1 < 2, do not swap

Fifth Iteration:

  • {1, 2, 3, 4, 5}; As the size of the array is 1, return.

Note: This is the base case.

Pseudo Code

void bubbleSort(arr[], n)
    if(n==1)
        return;

    for(i = 0; i<n-1; i++)
        if(arr[i] > arr[i+1])
            swap(arr[i], arr[i+1])

    bubbleSort(arr, n-1)

Implementations

Video Explanation

A video explaining iterative as well as recursive bubble sort