Question

Let P be a quicksort program to sort numbers in ascending order using the first element as the pivot. Let t₁ and t₂ be the number of comparisons made by P for the inputs [ 1 2 3 4 5] and [ 4 1 5 3 2] respectively . Which one of the following holds?

A. t₁ = 5
B. t₁ < t₂
C. t₁ = t₂
D. t₁ > t₂

Answer 1

The number of comparisons made by the quicksort program for the given inputs is the same. So the correct answer is option c.

Step-by-step explanation:

The given question is about a quicksort program to sort numbers in ascending order. Let's analyze the two inputs provided: [1 2 3 4 5] and [4 1 5 3 2].

1. For the input [1 2 3 4 5], the quicksort algorithm will choose the first element (1) as the pivot. This will result in comparing 1 with all the other elements (2, 3, 4, 5). So, a total of 4 comparisons will be made.
2. For the input [4 1 5 3 2], the quicksort algorithm will choose the first element (4) as the pivot. This will result in comparing 4 with all the other elements (1, 5, 3, 2). So, a total of 4 comparisons will be made.

From the above analysis, we can see that t₁ (number of comparisons for [1 2 3 4 5]) is equal to t₂ (number of comparisons for [4 1 5 3 2]). Therefore, the correct answer is C. t₁ = t₂.