Sorting

Use Bubble Sort on the list
$[7, 11, 3, 10, 17, 23, 1, 4, 21, 5]$.

- Pass 1: largest element moves to the end.
Result: $[7, 3, 10, 11, 17, 1, 4, 21, 5, 23]$
- Pass 2: next largest moves to its position.
Result: $[3, 7, 10, 11, 1, 4, 17, 5, 21, 23]$
- Pass 3: next largest moves to its position.
Result: $[3, 7, 10, 1, 4, 11, 5, 17, 21, 23]$

So after three complete passes, the partially sorted list is:
$[3, 7, 10, 1, 4, 11, 5, 17, 21, 23]$.

The list is $[63, 42, 21, 9]$.

## Selection sort
Selection sort places the smallest element at its correct position in each pass.

- Pass 1: smallest is $9$, swap with $63$ → 1 swap
- Pass 2: smallest of remaining $[42, 21, 63]$ is $21$, swap with $42$ → 1 swap
- Pass 3: smallest of remaining $[42, 63]$ is $42$, already in place → 0 swap

So, selection sort requires 2 swaps.

Number of comparisons in selection sort for $n=4$:
$3 + 2 + 1 = 6$

## Bubble sort
Bubble sort repeatedly compares adjacent elements and swaps if they are unordered.

For $[63, 42, 21, 9]$:
- Comparisons in pass 1: 3, swaps: 3
- Comparisons in pass 2: 2, swaps: 2
- Comparisons in pass 3: 1, swaps: 1

So, bubble sort requires 6 swaps.

Number of comparisons in bubble sort for $n=4$:
$3 + 2 + 1 = 6$

## Conclusion
- Selection sort swaps = 2
- Bubble sort swaps = 6
- With respect to the number of comparisons, both make 6 comparisons for 4 elements.
- But considering swaps, selection sort is better because it uses fewer swaps.

For Insertion Sort, the number of comparisons is minimum when the list is already in ascending order, because each new element is inserted without much shifting.

- List 1: $[2, 3, 5, 7, 11]$ is already sorted in ascending order.
- List 2: $[11, 7, 5, 3, 2]$ is in descending order, so every element must be compared and shifted.

Therefore, List 1 will make the minimum number of comparisons.

Diagrammatically:
- List 1: each element is already in correct order, so only direct checks are needed.
- List 2: each new element moves through the whole sorted part, causing many comparisons.