$2($a$)$ Complete the following implementation of recursive quicksort in

Java, including the partitioning algorithm. What is the complexity

of quicksort?

$($b$)$ Alice's ElGamal public key modp$)$ is $(23,11,2).$ Obtain

$[8$ marks$]$

her private key by brute force.

$($c$)$ Write a Java method which takes in an array of numbers and

$[9$ marks$]$

inserts them into a hash table so that their presence in the table

can be queried in $O(1)$ time. Assume that there is a class

variable called int $[]$ hashtable of size $9991$ which

represents the hash table. Select a collision resolution strategy

of your choice and explain how it works.