A disk has $300$ cylinders $(0$ to $299)$. If the initial position of the read-write head is at cylinder $101$, moving towards the higher end of the disk, calculate the total head movement following C_LOOK policy for the read request sequence:

$123,45,197,87,250,198,280$

Initial head position:

$101$

Direction is towards higher cylinder numbers.

Request sequence in sorted order:

$45,87,123,197,198,250,280$

Using C_LOOK, first serve higher side requests:

$101 \to 123 \to 197 \to 198 \to 250 \to 280$

Then jump to lowest request:

$280 \to 45$

Then continue:

$45 \to 87$

Total head movement:

$=|123-101|+|197-123|+|198-197|+|250-198|+|280-250|+|45-280|+|87-45|$

$=22+74+1+52+30+235+42$

$=456$

Correct option is:

$\boxed{(a)\ 456}$