What is a bubble sort in C++ and how is it implemented?

Table of Contents

• Introduction
• How Bubble Sort Works
  • 1. Basic Algorithm
  • 2. Passes and Swaps
• Bubble Sort Algorithm in C++
  • 1. Implementation of Bubble Sort
  • 2. Explanation
• Time Complexity and Efficiency
  • 1. Time Complexity
  • 2. Space Complexity
• Practical Example
  • 1. Sorting a List of Numbers
• Conclusion

Introduction

Bubble sort is one of the simplest sorting algorithms in C++. It repeatedly compares adjacent elements in an array and swaps them if they are in the wrong order. This process continues until the array is sorted. Although easy to understand and implement, bubble sort is not the most efficient algorithm for large datasets due to its time complexity of O(n²).

In this guide, we will explore the bubble sort algorithm, discuss its characteristics, and provide a detailed implementation in C++.

How Bubble Sort Works

1. Basic Algorithm

The bubble sort algorithm works by repeatedly stepping through the list and comparing adjacent elements. If an element is greater than the one next to it, the two elements are swapped. This "bubbling" of larger elements to the end of the array continues until the array is fully sorted.

2. Passes and Swaps

Each pass through the array pushes the largest unsorted element to its correct position. This is done by comparing each pair of adjacent elements and swapping them if necessary. The algorithm continues making passes until no more swaps are needed.

Bubble Sort Algorithm in C++

1. Implementation of Bubble Sort

2. Explanation

• Outer Loop: This loop tracks how many passes through the array have been made. After each pass, the largest unsorted element is placed in its correct position.
• Inner Loop: This loop compares adjacent elements. If the element on the left is greater than the one on the right, the two elements are swapped.
• Optimization: If no swaps occur during a pass, the array is already sorted, and the algorithm can terminate early, saving unnecessary iterations.

Time Complexity and Efficiency

1. Time Complexity

• Best-case time complexity: O(n) — If the array is already sorted, bubble sort can terminate early.
• Worst-case time complexity: O(n²) — When the array is sorted in reverse order, the algorithm must make n passes with n comparisons on each pass.
• Average-case time complexity: O(n²) — On average, bubble sort performs poorly for large datasets.

2. Space Complexity

• Space complexity: O(1) — Bubble sort is an in-place sorting algorithm, meaning it requires only a constant amount of additional memory.

Practical Example

1. Sorting a List of Numbers

Consider sorting a list of student grades from lowest to highest:

In this example, the student grades are sorted from lowest to highest using bubble sort.

Conclusion

Bubble sort is a simple yet inefficient sorting algorithm suitable for small datasets or cases where ease of implementation is a priority over performance. Despite its O(n²) time complexity, bubble sort can be optimized by detecting if the array is already sorted, making it slightly more efficient. However, for larger datasets, more advanced sorting algorithms like quicksort or mergesort are generally preferred. Understanding bubble sort is essential for grasping the basics of sorting in C++.