III.         Consider the following page-reference string in a demand paged memory scheme:

                           3, 8, 5, 8, 1, 2, 3, 4, 1, 8, 4, 2, 1, 3, 2, 4, 3, 8, 2, 5.

(a) Assuming only three frames exist in the main memory, how many page faults would occur for the following replacement algorithms? Note that initially, all the frames are empty.

(b) Assuming only four frames exist in the main memory, how many page faults would occur for the following replacement algorithms? Note that initially, all the frames are empty.

c)Optimal replacement

d)LRU replacement

For each case, you need to show all the steps in the form of a diagram 

Note that there are four cases.