Question $1-$ Page Replacement $(30$ points$)$

$($This question is related to ILO $3[$Performance$]-$ analyze and evaluate the algorithms and explain the major performance issues of OS$.)$

Consider a computer system with a main memory consisting of $4$ frames and a page table for tracking the pages in the memory. The following sequence of page references is given:

$\backslash [$

$3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3,2,3,8,4$

$\backslash ]$

Assume that initially, the memory is empty. You are required to simulate the page replacement process and determine the number of page faults that occur using the following page replacement algorithm.

If there is a tie in the selection process, you can assume that the oldest page will be replaced in order to break the tie. Solve the problem by showing the sequence of page faults and the pages present in the memory after each reference.

$($a$)(15$ points$)$ Using the Least Frequently Used $($LFU$)$ algorithm.

$($b$)(15$ points$)$ Using the Clock Replacement algorithm.