$6\mathrm{.}5$ Given the following state for the Banker's algorithim: $6$ processes p$0$ through p$5$

$4$ resources types: A$(15$ instances$)$; B$(6$ instances$)$; C$(9$instances$)$; D$(10$ instances$)$

Snapshot at time T$0$:

Available

A B C D

$6354$

The first four columns of the $68$ matrix comprise the Allocation matrix. The final four

columns comprise the Claim matrix. The Need matrix referred to in part $($b$)$ is the same

as the $C-$A matrix described in the text.

a$.$ Verify that the Available array has been correctly calculated.

b$.$ Calculate the Need matrix.

c$.$ Show that the current state is safe, that is$,$ show a safe sequence of processes. In

addition, to the sequence show how the Available $($working array$)$ changes as each

process terminates.

d$.$ Given the request $(3,2,3,3)$ from Process P$5.$ Should this request be granted? Why

or why not?

$6\mathrm{.}6.$ In the code below, three processes are competing for six resources labeled A to F$.$

a$.$ Using a resource allocation graph $($see Figures $6\mathrm{.}5$ and $6\mathrm{.}6),$ show the possibility of

a deadlock in this implementation.

b$.$ Modify the order of some of the get requests to prevent the possibility of any dead$-$

lock. You cannot move requests across procedures, only change the order inside

each procedure. Use a resource allocation graph to justify your answer.