Q$2)$ Consider a computer system involving $4$ processes $(P1,P2,P3,P4$ and $5$ different types of resources $($R$1,$ R$2,$ R$3,$ R$4,$ R$5).$ Assume that $2$ instances of R$1,1$ instance of R$2,1$ instance of R$3,2$ instances of R$4,$ and $1$ instance of R$5$ exist.

$\backslash$table$[[,$Allocation,Request $/$ Need,MAX,Available$],[,$R$1,R2,$R$1,$R$4,$R$5,$R$1,R2,$R$3,$R$4,$R$5,$R$1,R2,$R$3,$R$4,$RS$,$R$1,R2,$R$3,$R$4,$R$5],[$P$1,1,0,1,1,0,0,1,0,0,1,,,,,,,,,,],[$P$2,1,1,0,0,0,1,0,1,0,1,,,,,,,,,,],[$P$3,0,0,0,1,0,0,0,0,0,1,,,,,,,,,,],[$P$4,0,0,0,0,0,0,0,0,1,1,,,,,,,,,,]]$

a$)$ Fill in the max and available vector.

b$)$ Apply the deadlock detection algorithm to show whether there is a deadlock or not. Clearly show the applied steps and do the necessary explanations.