What is Bubble Sort, and How Exactly Does it Work?

Have you ever wondered how computers organize and sort vast amounts of data? Think about the contacts in your phone, arranged alphabetically, or an e-commerce site that quickly sorts products by price. At the heart of these processes are sorting algorithms, and one of the simplest yet foundational ones is Bubble Sort.

But how does Bubble Sort really work? What makes it bubble, and why is it often considered an essential starting point in learning algorithms? Let’s dive in and explore its workings, key concepts, and practical applications!

In this blog, we will delve into the Bubble Sort algorithm, exploring its key concepts, practical tips, and strategies to optimize its performance.

Key Points or Concepts Related to Bubble Sort

What is Bubble Sort?

Bubble Sort is a simple comparison-based sorting algorithm. It repeatedly steps through the list, compares adjacent elements, and swaps them if they are in the wrong order. This process continues until the list is fully sorted, with larger elements “bubbling up” to their correct position at the end of the list, hence the name “Bubble Sort.”

How Does Bubble Sort Work?

The algorithm operates by comparing each pair of adjacent elements in the array and swapping them if the first element is larger than the second. It repeatedly goes through the array until no more swaps are needed, indicating that the array is sorted.

Algorithm Steps:

1. Start at the beginning of the array.
2. Compare the first element with the next one.
3. If the first element is larger than the next, swap them.
4. Move to the next element and repeat the process.
5. After each pass, the largest unsorted element will be placed at the end of the array.
6. Repeat the process for the rest of the elements until the array is sorted.

Curious how? Here’s a simple example:

Let’s say you have the following array:

array[] = [5, 3, 8, 4, 2]

Step 1: First Pass

1. Compare 5 and 3: Since 5 > 3, swap them.
   • List: [3, 5, 8, 4, 2]
2. Compare 5 and 8: No swap needed.
   • List: [3, 5, 8, 4, 2]
3. Compare 8 and 4: Since 8 > 4, swap them.
   • List: [3, 5, 4, 8, 2]
4. Compare 8 and 2: Since 8 > 2, swap them.
   • List: [3, 5, 4, 2, 8]

At the end of the first pass, the largest element (8) has “bubbled” to its correct position at the end of the list.

Step 2: Second Pass

1. Compare 3 and 5: No swap needed.
   • List: [3, 5, 4, 2, 8]
2. Compare 5 and 4: Since 5 > 4, swap them.
   • List: [3, 4, 5, 2, 8]
3. Compare 5 and 2: Since 5 > 2, swap them
   • List: [3, 4, 2, 5, 8]
4. Compare 5 and 8: No swap needed.
   • List: [3, 4, 2, 5, 8]

By the end of the second pass, the next largest element (5) is in its correct position.

Continuing the Process

The process continues with each pass through the list until no swaps are needed, indicating that the list is sorted. For our example, further passes will eventually sort the list completely to:

[2, 3, 4, 5, 8]

Problem Statement: 

Given an array of N Integers, write a program to implement the Bubble Sorting algorithm.

Examples:

Input: N=6, array [ ] = {13,46,24,52,20,9}

Output: 9,13,20,24,46,52

Explanation: After sorting we get 9,13,20,24,46,52

Input: N = 5, array [ ] = {5,4,3,2,1}

Output: 1,2,3,4,5

Explanation: After sorting we get 1,2,3,4,5

Dry Run:

Iteration 1:

Iteration 2:

Iteration 3: 

Iteration 4:

Iteration 5:

Complexity:

• Time Complexity: The worst and average-case time complexity of Bubble Sort is O(N²), where N is the number of elements in the array. This happens because each pass through the array involves comparing and potentially swapping adjacent elements, and this must be repeated N times.
• Space Complexity: Bubble Sort is an in-place algorithm, meaning it requires only O(1) extra space for temporary storage.

Practical Tips or Strategies for Implementing Bubble Sort

Though Bubble Sort is conceptually simple, here are a few tips and strategies to make its implementation more efficient:

1. Optimize for Best Case Scenario:

If the array is already sorted, Bubble Sort can be optimized to avoid unnecessary passes. By introducing a flag variable that keeps track of whether any swaps were made during a pass, we can terminate the algorithm early if no swaps occur. This reduces the best-case time complexity to O(N).

Bubble Sort Algorithm

Here’s a simple implementation of Bubble Sort in Python:

#include <bits/stdc++.h>
using namespace std;

void bubble_sort(int arr[], int n) {
    // bubble sort
    for (int i = n - 1; i >= 0; i--) {
        for (int j = 0; j <= i - 1; j++) {
            if (arr[j] > arr[j + 1]) {
                int temp = arr[j + 1];
                arr[j + 1] = arr[j];
                arr[j] = temp;
            }
        }
    }

    cout << "After Using bubble sort: " << "\n";
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
    cout << "\n";
}

int main()
{
    int arr[] = {13, 46, 24, 52, 20, 9};
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << "Before Using Bubble Sort: " << endl;
    for (int i = 0; i < n; i++)
    {
        cout << arr[i] << " ";
    }
    cout << endl;

    bubble_sort(arr, n);
    return 0;

}

Output:

Before Using Bubble Sort:
13 46 24 52 20 9
After Using bubble sort:
9 13 20 24 46 52

Time complexity: O(N²), (where N = size of the array), for the worst, and average cases.
Reason: If we carefully observe, we can notice that the outer loop, say i, is running from n-1 to 0 i.e. n times, and for each i, the inner loop j runs from 0 to i-1. For, i = n-1, the inner loop runs n-1 times, for i = n-2, the inner loop runs n-2 times, and so on. So, the total steps will be approximately the following: (n-1) + (n-2) + (n-3) + ……..+ 3 + 2 + 1. The summation is approximately the sum of the first n natural numbers i.e. (n*(n+1))/2. The precise time complexity will be O(n²/2 + n/2). Previously, we have learned that we can ignore the lower values as well as the constant coefficients. So, the time complexity is O(n²). Here the value of n is N i.e. the size of the array.

Space Complexity: O(1)

2. Avoid Redundant Comparisons:

After each pass, the largest element is already sorted, so we can avoid checking those elements again. Hence, after each outer loop iteration, the range of elements to be checked decreases by one.

3. Use for Small Arrays or Nearly Sorted Data:

Due to its O(N²) time complexity, Bubble Sort is not efficient for large datasets. However, it works well for small arrays or arrays that are almost sorted, where a few passes will sort the array completely.

Practical Applications of Bubble Sort

Even though Bubble Sort is not used in production-level software due to its inefficiency, it is useful in specific situations:

1. Teaching Tool: It’s widely used as an introductory algorithm to help students understand the fundamental concept of sorting.
2. Small Data Sorting: When the dataset is very small or nearly sorted, Bubble Sort can perform reasonably well.
3. Detecting Early Termination: In systems where an already sorted array is likely, Bubble Sort can detect if the array is already sorted in just one pass, making it an efficient option in those scenarios.

Conclusion: Summarizing Key Points

Bubble Sort is a straightforward yet inefficient sorting algorithm for large datasets. It operates by comparing adjacent elements and swapping them if needed, effectively pushing larger elements to the end of the list. While its O(N²) time complexity makes it unsuitable for big data applications, it remains a useful algorithm for teaching purposes and smaller, nearly sorted datasets.

By optimizing the algorithm with a flag variable to detect if a list is already sorted, you can improve its performance to O(N) in the best case. However, for more performance-sensitive applications, more advanced algorithms like Quick Sort or Merge Sort are preferred.

If you are new to data structures and algorithms, Bubble Sort is an excellent starting point. Try implementing it yourself and experiment with different datasets to see how it performs.

For more advanced sorting techniques, continue exploring algorithms like Quick Sort and Merge Sort.