Question $2.$ Virtual Memory, Page Replacement $(20$ pts$.)$

Consider pure demand paging as fetch policy. A process contains seven virtual pages $(0,1,2,3,4,5,6)$ on disk and is assigned to a fixed allocation of three page frames $(0,1,2)$ in main memory which are initially empty. Consider the following reference string: $3,4,5,6,3,1,1,2,5,2,5,1,6,2,1,2,4,3,2,5.$ Show the successive page residing in the three frames using the Optimal and Least Recently Used $($LRU$)$ policies starting with an empty main memory. How many page faults would occur in each case?

Optimal Policy

$\backslash$table$[[$Ref$.$ string $,3,4,5,6,3,1,1,2,5,2,5,1,6,2,1,2,4,3,2,5$