please give correct answer only and do not use AI or chatgpt.

$($a$)$ Write a program that implements the FIFO, LRU, and optimal page replacement algorithms using random page$-$reference string where page numbers range from $0$ to $9.$

$($b$)$ Apply the random page$-$reference string to each algorithm, and record the number of page faults incurred by each algorithm. Implement the replacement algorithms so that the number of page frames can vary from $1$ to $7.$ Assume that demand paging is used.

$($c$)$ Compare the performance of three algorithms on a generated virtual traces.