$2$ Banker's Algorithm $($Resource Allocation Denial$)$

Given the following state for the Banker's Algorithm.

$5$ processes P$0$ through P$4$

$4$ resource types $A(12$ instances$)$; B $(7$ instances$)$ C $(5$ instances$)$; D $(8$ instances$)$

and the following snapshot at time T$0$:

Available

$\{$:$V=[A,B,C,D],[5,3,3,3])$

Allocation

$A=\{\begin{array}{c}\text{:}[]\\ P_0\\ P_1\\ P_2\\ P_3\\ P_4\end{array}([2,1,0,1],[0,1,1,1],[3,1,0,2],[1,0,1,1],[1,1,0,0])$

Maximum Claim

$C=\{\begin{array}{c}\text{:}[]\\ P_0\\ P_1\\ P_2\\ P_3\\ P_4\end{array}([A,B,C,D],[2,5,5,5],[7,5,3,3],[3,3,3,2],[5,2,2,1])$

Questions

Verify that the Available array has been calculated correctly.

Calculate the Need matrix.

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.

Given a request from P$1$ for the additional resources $(2,1,2,2)$ to be allocated in addition to

P$1\text{'}$s current allocations, should this request be granted? Why or why not?