Understanding the Bubble Sort Algorithm with an Example

Bubble Sort is one of the simplest sorting algorithms in computer science. Its straightforward approach makes it an excellent starting point for beginners learning about sorting techniques. Despite being easy to understand, Bubble Sort is not the most efficient for large datasets. In this article, we’ll explore how Bubble Sort works with a practical example.

What is Bubble Sort?

Bubble Sort is a comparison-based algorithm where each pair of adjacent elements is compared, and their positions are swapped if they are in the wrong order. This process repeats for every element in the array until the entire array is sorted.

Key Characteristics:

• Algorithm Type: Comparison-based, stable.
• Time Complexity:
  • Best Case: O(n) (when the array is already sorted).
  • Worst Case: O(n^2) (when the array is sorted in reverse order).
• Space Complexity: O(1) (in-place sorting).

Bubble Sort Algorithm Steps

1. Compare adjacent elements.
2. Swap them if they are in the wrong order.
3. Repeat steps 1 and 2 for all elements until no swaps are required in a complete pass.

Bubble Sort Example: Sorting [5, 3, 8, 6, 2]

Let’s sort the array [5, 3, 8, 6, 2] in ascending order using Bubble Sort. We’ll go through each pass step-by-step.

Initial Array:

[ 5, 3, 8, 6, 2 ]

Pass 1

1. Compare 5 and 3. Swap them because 5 > 3.
   Array: [ 3, 5, 8, 6, 2 ]
2. Compare 5 and 8. No swap needed because 5 < 8. Array: [ 3, 5, 8, 6, 2 ]
3. Compare 8 and 6. Swap them because 8 > 6.
   Array: [ 3, 5, 6, 8, 2 ]
4. Compare 8 and 2. Swap them because 8 > 2.
   Array: [ 3, 5, 6, 2, 8 ]

Pass 2

1. Compare 3 and 5. No swap needed because 3 < 5. Array: [ 3, 5, 6, 2, 8 ]
2. Compare 5 and 6. No swap needed because 5 < 6. Array: [ 3, 5, 6, 2, 8 ]
3. Compare 6 and 2. Swap them because 6 > 2.
   Array: [ 3, 5, 2, 6, 8 ]

Pass 3

1. Compare 3 and 5. No swap needed because 3 < 5. Array: [ 3, 5, 2, 6, 8 ]
2. Compare 5 and 2. Swap them because 5 > 2.
   Array: [ 3, 2, 5, 6, 8 ]

Pass 4

1. Compare 3 and 2. Swap them because 3 > 2.
   Array: [ 2, 3, 5, 6, 8 ]

Now the array is sorted, and no further passes are required.

Visualization of Bubble Sort

Here’s a step-by-step representation:

Pros and Cons of Bubble Sort

Advantages:

• Easy to understand and implement.
• Requires minimal memory (in-place sorting).

Disadvantages:

• Inefficient for large datasets due to O(n^2) complexity.
• Performs unnecessary passes even when the array is sorted (can be optimized with a flag).

Optimized Bubble Sort

To improve efficiency, we can introduce a flag that tracks whether any swaps occurred during a pass. If no swaps are made, the array is already sorted, and the algorithm can terminate early.

Conclusion

Bubble Sort is a fundamental algorithm that demonstrates basic sorting principles. While it is not suitable for performance-critical applications, its simplicity makes it a valuable educational tool for understanding the mechanics of sorting algorithms. For more efficient sorting, algorithms like Quick Sort or Merge Sort are better options.