Bubble Sort

Sorting algorithms are fundamental components of computer science. They organize an array of data into a particular order, facilitating quicker and more effective data processing. This can be critical in many areas, from database operations to machine learning algorithms.

Among the wide array of sorting algorithms, Bubble Sort holds a unique position due to its simplicity and ease of understanding.

It is a straightforward sorting algorithm that operates by repeatedly comparing pairs of adjacent elements and swapping them if they are in the wrong order. This process continues throughout the entire list until no more swaps are necessary, indicating that the list is fully sorted.

A distinctive characteristic of Bubble Sort is the way it “bubbles” the larger elements toward the end of the array, which is how it earned its name.

How it works

Imagine having a list of numbers. The algorithm starts at the beginning of the list and compares the first two numbers. If the first number is bigger than the second, it swaps them. Then it moves to the next number and does the same thing, and continues to do so until it reaches the end of the list. This completes a single pass through the list.

After the first pass, the largest number will have "bubbled" to the end of the list. The process is then repeated for the rest of the list, except for the last element, then the second last, and so on, until you get to the start of the list.

Here is a simple implementation in C#:

public void BubbleSort(int[] arr)
{
    var n = arr.Length - 1;

    for (var i = 0; i < n; i++)
    {
        for (var j = 0; j < n - i; j++)
        {
            if (arr[j] > arr[j + 1])
            {
                (arr[j], arr[j + 1]) = (arr[j + 1], arr[j]);
            }
        }
    }
}

Time complexity

It has a time complexity of O(n²) in both the worst-case and average-case scenarios, where n is the number of elements to be sorted. This means that the execution time for the algorithm increases quadratically with the size of the input.

Even in the best-case scenario, when the list is already sorted, Bubble Sort still has a time complexity of O(n). This is because the algorithm doesn't recognize the sorted state after the first pass and has to perform all the passes.

Space complexity

Since this is a stable in-place sorting algorithm, it needs only a constant amount of additional space to perform the sorting O(1). Sorting is performed directly on the input data structure, which makes it space-efficient.

Conclusion

Despite its limitations, Bubble Sort holds a special place in the vast realm of sorting algorithms. Its simplicity makes it an ideal starting point for learning about sorting algorithms, and its unique "bubbling" mechanism provides valuable insight into how data can be manipulated.

While it may not be the optimal choice for large datasets or time-critical applications, it is perfect for small or nearly sorted datasets. Moreover, its concept has been foundational in the development of more advanced sorting algorithms.

In the world of computer science education, Bubble Sort continues to "bubble up" fostering new generations of learners to explore, understand, and innovate.

References

• Algoritmi e programmazione in C di Francesco Oliveri, Aracne editrice (Italian book)