Assume that we use Quicksort to sort the array A with $5$ elements where the initial values of

the array elements $($indexed from $1$ to $5)$ are A: $3402101.$

This question tests your understanding of the algorithm by following the element$-$wise

comparisons made in the execution of the algorithm. Here an element$-$wise comparison

means the comparison of one element of the array with another element of the array or the

key set in a particular step of the algorithm $($Line $4$ in Partition$).$

Since the algorithm may move the elements of the array, you are asked to show the values of

the elements being compared.

The first element$-$wise comparison is $31?$

In order to answer the question correctly, you need to execute the algorithm on the given

input step by step. The Quicksort algorithm here refers to the one taught in this class.

$($a$)$ What is the $2$nd element$-$wise comparison?

$($b$)$ What is the $3$rd element$-$wise comparison?

$($c$)$ What is the $5$th element$-$wise comparison?

$($d$)$ What is the $7$th element$-$wise comparison?