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Understanding Bubble Sort: The Simplest Sorting Algorithm

Understanding Bubble Sort: The Simplest Sorting Algorithm

Aaqib Bashir Mir's photo
Aaqib Bashir Mir
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3 min read

Bubble Sort is one of the most basic and widely taught sorting algorithms. Although not the most efficient, its simplicity makes it a great starting point for anyone new to algorithms. Let’s dive into the concept, implementation, and analysis of Bubble Sort.

What is Bubble Sort?

Bubble Sort is a 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 sorted.

The name "Bubble Sort" comes from the way larger elements "bubble up" to the end of the list through successive swaps.

How Does Bubble Sort Work?

  1. Start at the beginning of the array.

  2. Compare the first two elements:

    • If the first element is greater than the second, swap them.

  3. Move to the next pair and repeat step 2.

  4. Continue this process until the largest element is "bubbled" to its correct position at the end of the array.

  5. Repeat the process for the remaining unsorted portion of the array.

  6. Stop when no swaps are needed, indicating that the array is sorted.

Step-by-Step Example

Let’s sort the array: [5, 3, 8, 6, 2]

Pass 1:

  • Compare 5 and 3 → Swap → [3, 5, 8, 6, 2]

  • Compare 5 and 8 → No Swap → [3, 5, 8, 6, 2]

  • Compare 8 and 6 → Swap → [3, 5, 6, 8, 2]

  • Compare 8 and 2 → Swap → [3, 5, 6, 2, 8]

Largest element (8) is now at the end.

Pass 2:

  • Compare 3 and 5 → No Swap → [3, 5, 6, 2, 8]

  • Compare 5 and 6 → No Swap → [3, 5, 6, 2, 8]

  • Compare 6 and 2 → Swap → [3, 5, 2, 6, 8]

Second largest element (6) is now in its correct position.

Pass 3:

  • Compare 3 and 5 → No Swap → [3, 5, 2, 6, 8]

  • Compare 5 and 2 → Swap → [3, 2, 5, 6, 8]

Pass 4:

  • Compare 3 and 2 → Swap → [2, 3, 5, 6, 8]

Now the array is sorted.

Bubble Sort Algorithm in Python

Here’s how you can implement Bubble Sort:

def bubble_sort(arr):
    n = len(arr)
    for i in range(n - 1):
        # Flag to check if any swaps happened
        swapped = False
        for j in range(n - 1 - i):
            if arr[j] > arr[j + 1]:
                # Swap if elements are out of order
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
                swapped = True
        # If no swaps, the array is already sorted
        if not swapped:
            break
    return arr

# Example usage
array = [5, 3, 8, 6, 2]
print("Sorted Array:", bubble_sort(array))

Complexity Analysis

  1. Time Complexity:

    • Best Case (Already Sorted): O(n)

    • Average Case: O(n²)

    • Worst Case (Reversed Array): O(n²)

  2. Space Complexity:

    • O(1): Bubble Sort is an in-place sorting algorithm, requiring no additional space.

When to Use Bubble Sort?

While Bubble Sort isn’t the most efficient, it’s ideal for:

  • Teaching basic sorting concepts.

  • Small datasets where performance isn’t critical.

  • Situations where simplicity is preferred over efficiency.

Conclusion

Bubble Sort may not be the fastest sorting algorithm, but it’s intuitive approach to sorting makes it a must-know for beginners. Mastering it lays the foundation for understanding more complex algorithms like Quick Sort or Merge Sort.

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