Clock Beats LRU

Three frames, initially empty. Reference string:

2, 3, 1, 2, 4, 3, 5, 2, 1, 4

The clock variant is the standard one: frames are numbered f0, f1, f2 and filled in that order while any are empty, the hand is left pointing just past the frame it last filled, a reference sets that frame's use bit, and on a fault the hand advances, clearing each use bit it finds set, until it reaches a frame whose use bit is already 0 and evicts it.

The clock hand sweeps three frames, clearing use bits until it finds a zero f0 f1 f2 use bit 1: clear it, move on use bit 0: evict this frame

How many page faults do optimal, clock and LRU take on this string?

A

optimal 5, clock 8, LRU 9

B

optimal 6, clock 8, LRU 9

C

optimal 6, clock 9, LRU 8

D

optimal 6, clock 9, LRU 9