Understanding Bubble Sort: A Step-by-Step Guide with Practical Examples

Bubble sort is a simple sorting algorithm that repeatedly steps through a list, compares adjacent elements, and swaps them if they are in the wrong order. This process is repeated until the list is sorted. Despite its simplicity, bubble sort is not efficient for large datasets, but it is useful for educational purposes and small datasets.

How Bubble Sort Works: A Detailed Explanation

The basic idea behind the bubble sort is straightforward: smaller elements gradually move towards the beginning of the list, while larger elements move to the end. Here's a detailed explanation:

Step-by-Step Guide

Starting from the first element: Compare the current element with the next element. If the current element is greater than the next element, swap them. Move to the next element and repeat the comparison until the end of the array is reached. After each complete pass through the array, the largest element will have moved to its correct position at the end. Repeat the entire process for the remaining unsorted elements: Continue the process until no more swaps are needed.

Example: Sorting an Array

Consider the array: [5, 2, 9, 1, 5, 6].

Pass 1

Compare 5 and 2 → swap → [2, 5, 9, 1, 5, 6]. Compare 5 and 9 → no swap. Compare 9 and 1 → swap → [2, 5, 1, 9, 5, 6]. Compare 9 and 5 → swap → [2, 5, 1, 5, 9, 6]. Compare 9 and 6 → swap → [2, 5, 1, 5, 6, 9].

Pass 2

Compare 2 and 5 → no swap. Compare 5 and 1 → swap → [2, 1, 5, 5, 6, 9]. Compare 5 and 5 → no swap. Compare 5 and 6 → no swap. Compare 6 and 9 → no swap.

This process continues until the array is fully sorted.

Characteristics of Bubble Sort

The performance of bubble sort can be described using time and space complexity:

Time Complexity

Worst-case: On2 Average case: On2 Best case: On when the array is already sorted

Space Complexity

Bubble sort is an in-place sorting algorithm with a space complexity of O1.

Use Cases for Bubble Sort

Bubble sort is easy to understand and implement, making it a good educational tool. However, it is not suitable for large datasets due to its poor performance compared to more advanced algorithms like quicksort or mergesort. It can be useful for sorting small datasets or for teaching the concept of sorting algorithms.

Comparison-Based Sorting Algorithm

Bubble sort is a type of comparison-based sorting algorithm. It repeatedly compares pairs of adjacent items and swaps them if they are in the wrong order. This process is repeated until the list is fully sorted.

Algorithm Behavior

Using the bubble sort method, a string of numbers or items can be placed in the correct order. Starting from the left and moving right, each group of adjacent components is examined and rearranged if necessary.

In an ideal scenario, the algorithm would sort two items at a time, ensuring that they are in ascending order before continuing the process and completing a pass without moving any numbers. This method is particularly useful for datasets that are not extremely large.

Conclusion

Bubble sort, although simple to understand and implement, is not recommended for sorting large datasets due to its high time complexity. It is, however, a valuable tool for small datasets and for educational purposes, as it clearly illustrates the basic principles of sorting algorithms.