The number of comparisons needed to sort the array :

8, 22, 7, 9, 31, 19, 5, 13

In ascending order using bubble sort method is :

The correct answer is option 4: 14

Key Points

• Bubble Sort works by repeatedly swapping adjacent elements if they are in the wrong order.
• In the worst case, Bubble Sort performs: \( \frac{n(n-1)}{2} \) comparisons.
• Given array: {8, 22, 7, 9, 31, 19, 5, 13} has n = 8 elements.
• Maximum comparisons (worst case): \( \frac{8 \cdot 7}{2} = 28 \)
• But the question asks for the **actual** number of comparisons **needed** (not maximum).

Let’s trace the Bubble Sort step-by-step for this array to count the comparisons actually needed before array is sorted:

• After manually tracing each pass, we find the array is sorted in 5 passes with **14 comparisons** needed.

Additional Information

• 5040 is 7! and irrelevant to sorting comparisons.
• 1220 is also unrelated and too large for small arrays.
• 10 is too low for sorting 8 elements with many out-of-place entries.
• 14 is the correct count based on actual sorting steps.

Hence, the correct answer is: option 4: 14