Bubble & Selection Sorts

Comparison of Bubble Sort and Selection Sort

Example: Implementing Sorting Algorithms

Algorithm Steps

1. Bubble Sort
   1. Let r mark the right boundary of the unsorted part (initially r = n - 1).
   2. For j = 0..r-1, compare adjacent pairs a[j] and a[j+1]; swap if out of order.
   3. After the pass, the largest value in 0..r has bubbled to position r.
   4. Decrease r by 1 and repeat until a pass makes no swaps (or r == 0).
2. Selection Sort
   1. Let i mark the boundary; the unsorted part is i..n-1 (initially i = 0).
   2. Find the index of the smallest element in i..n-1.
   3. Swap that element with the one at position i.
   4. Increase i by 1 and repeat until i == n.

Bubble Sort Implementation

The classic implementation of a Bubble Sort is to use nested counted loops; i.e. nested FOR...TO...NEXT loops.

• Python
• Java

Refined Bubble Sort Implementation

It is possible to fine-tune Bubble Sort: stop early if a full pass makes no swaps, and shrink the inner loop’s upper bound to the index of the last swap. These tweaks improve performance on nearly sorted data.

• Python
• Java

def bubble_sort_refined(arr):
    """
    Tweaks:
      1) Early exit if an entire pass makes no swaps.
      2) Reduce the inner loop's upper bound to the last swap index.
    """
    n = len(arr)
    comparisons = 0
    swaps = 0

    while n > 1:
        last_swap = 0
        for j in range(n - 1):
            comparisons += 1
            if arr[j] > arr[j + 1]:
                arr[j], arr[j + 1] = arr[j + 1], arr[j]
                swaps += 1
                last_swap = j + 1  # everything after this is already in place for this pass
        if last_swap == 0:
            print("Early exit: no swaps on last pass")
            break
        n = last_swap  # next pass only needs to bubble up to the last swap point

    print(f"Comparisons: {comparisons}, Swaps: {swaps}")
    return arr

numbers = [64, 34, 25, 12, 22, 11, 90]
print("Sorted Array:", bubble_sort_refined(numbers))

import java.util.Arrays;

public class BubbleSortRefined {
    public static int[] bubbleSortRefined(int[] arr) {
        int n = arr.length;
        int comparisons = 0, swaps = 0;

        while (n > 1) {
            int lastSwap = 0;
            for (int j = 0; j < n - 1; j++) {
                comparisons++;
                if (arr[j] > arr[j + 1]) {
                    int tmp = arr[j];
                    arr[j] = arr[j + 1];
                    arr[j + 1] = tmp;
                    swaps++;
                    lastSwap = j + 1; // elements after this are already in place for this pass
                }
            }
            if (lastSwap == 0) {
                System.out.println("Early exit: no swaps on last pass");
                break;
            }
            n = lastSwap; // shrink upper bound to the last swap index
        }

        System.out.println("Comparisons: " + comparisons + ", Swaps: " + swaps);
        return arr;
    }

    public static void main(String[] args) {
        int[] numbers = {64, 34, 25, 12, 22, 11, 90};
        bubbleSortRefined(numbers);
        System.out.println("Sorted Array: " + Arrays.toString(numbers));
    }
}

Selection Sort Implementation

• Python
• Java

Choosing the Right Sorting Algorithm

• Use Bubble Sort when:
  • Dataset is small.
  • Data is almost sorted, minimising swaps.
• Use Selection Sort when:
  • Swapping is costly (e.g. limited write cycles).
  • Dataset is small and simplicity is preferred.