Q.Consider a list of 10 elements:
numList =[7,11,3,10,17,23,1,4,21,5].
Display the partially sorted list after three complete passes of Bubble sort.

This is a plain theory question that asks for a specific output after a fixed number of passes of Bubble Sort.

Understanding Bubble Sort

Bubble Sort works by repeatedly stepping through the list, comparing adjacent elements, and swapping them if they are in the wrong order. After each complete pass, the largest remaining unsorted element "bubbles up" to its correct position at the end of the list.

For a list of $n$ elements, you need at most $n-1$ passes to fully sort it. Here, $n = 10$, so after 3 passes, the last 3 elements (the three largest) will be in their final sorted positions.

Step-by-step execution

Initial list:

[7, 11, 3, 10, 17, 23, 1, 4, 21, 5]

Pass 1 (largest element — 23 — goes to the end)

Compare and swap where needed:

• 7 vs 11 → no swap → [7, 11, 3, 10, 17, 23, 1, 4, 21, 5]
• 11 vs 3 → swap → [7, 3, 11, 10, 17, 23, 1, 4, 21, 5]
• 11 vs 10 → swap → [7, 3, 10, 11, 17, 23, 1, 4, 21, 5]
• 11 vs 17 → no swap → [7, 3, 10, 11, 17, 23, 1, 4, 21, 5]
• 17 vs 23 → no swap → [7, 3, 10, 11, 17, 23, 1, 4, 21, 5]
• 23 vs 1 → swap → [7, 3, 10, 11, 17, 1, 23, 4, 21, 5]
• 23 vs 4 → swap → [7, 3, 10, 11, 17, 1, 4, 23, 21, 5]
• 23 vs 21 → swap → [7, 3, 10, 11, 17, 1, 4, 21, 23, 5]
• 23 vs 5 → swap → [7, 3, 10, 11, 17, 1, 4, 21, 5, 23]

After Pass 1: [7, 3, 10, 11, 17, 1, 4, 21, 5, **23**]

Pass 2 (second largest — 21 — goes to position 9)

• 7 vs 3 → swap → [3, 7, 10, 11, 17, 1, 4, 21, 5, 23]
• 7 vs 10 → no swap → [3, 7, 10, 11, 17, 1, 4, 21, 5, 23]
• 10 vs 11 → no swap → [3, 7, 10, 11, 17, 1, 4, 21, 5, 23]
• 11 vs 17 → no swap → [3, 7, 10, 11, 17, 1, 4, 21, 5, 23]
• 17 vs 1 → swap → [3, 7, 10, 11, 1, 17, 4, 21, 5, 23]
• 17 vs 4 → swap → [3, 7, 10, 11, 1, 4, 17, 21, 5, 23]
• 17 vs 21 → no swap → [3, 7, 10, 11, 1, 4, 17, 21, 5, 23]
• 21 vs 5 → swap → [3, 7, 10, 11, 1, 4, 17, 5, 21, 23]

After Pass 2: [3, 7, 10, 11, 1, 4, 17, 5, **21**, **23**]

Pass 3 (third largest — 17 — goes to position 8)

• 3 vs 7 → no swap → [3, 7, 10, 11, 1, 4, 17, 5, 21, 23]
• 7 vs 10 → no swap → [3, 7, 10, 11, 1, 4, 17, 5, 21, 23]
• 10 vs 11 → no swap → [3, 7, 10, 11, 1, 4, 17, 5, 21, 23]
• 11 vs 1 → swap → [3, 7, 10, 1, 11, 4, 17, 5, 21, 23]
• 11 vs 4 → swap → [3, 7, 10, 1, 4, 11, 17, 5, 21, 23]
• 11 vs 17 → no swap → [3, 7, 10, 1, 4, 11, 17, 5, 21, 23]
• 17 vs 5 → swap → [3, 7, 10, 1, 4, 11, 5, 17, 21, 23]

After Pass 3: [3, 7, 10, 1, 4, 11, 5, **17**, **21**, **23**]

Why Bubble Sort Passes?

Bubble sort works by making multiple passes through the list. In each pass, it compares adjacent elements and swaps them if they are in the wrong order. The key insight: after the first complete pass, the largest element ends up at the last position. After the second pass, the second-largest ends up at the second-last position, and so on. So after three passes, the three largest numbers are correctly placed at the end of the list.

Let's trace the passes step by step.

Initial list: [7, 11, 3, 10, 17, 23, 1, 4, 21, 5]

Pass 1 (largest element 23 bubbles to position 9)

After Pass 1: [7, 3, 10, 11, 17, 1, 4, 21, 5, 23]

Pass 2 (second-largest 21 bubbles to position 8)

After Pass 2: [3, 7, 10, 11, 1, 4, 17, 5, 21, 23]

Pass 3 (third-largest 17 bubbles to position 7)

After Pass 3: [3, 7, 10, 1, 4, 11, 5, 17, 21, 23]