Considering a system with five processes $P0$ through $P4$ and three resources types $A,B,C.$ Resource type A has $9$ instances, B has $6$ instances and type C has $6$ instances. Suppose at time $t_0$ following snapshot of the system has been taken:

$\backslash$table$[[$Process$,$Allocation,Max,Available$],[$A$,$B$,$C$,$A$,$B$,$C$,$A$,$B$,$C$,],[$P$0,1,1,1,3,3,2,2,2,2,],[$P$1,2,1,1,4,3,1,,,,],[$P$2,1,1,1,2,1,1,,,,],[$P$3,0,1,0,1,2,2,,,,],[$P$4,3,0,1,3,3,4,,,,]]$

By applying banker's algorithm

i$.$ What will be the content of need matrix? ii$.$ Is the system in safe state? If yes, then what is the safe sequence?

$2.$ Consider the following page reference string:

$1,3,2,3,4,2,1,3,4,2,1,2,5,1,3.$

How many page faults would occur for the least recently used algorithm $($LRU$),$ assuming three frames?

$3.$ Calculate average waiting time and draw Gantt chart for the following table using Shortest Job First Preemptive method.

$\backslash$table$[[$Process$,$Burst Time,Arrival Time$],[$P$1,5,0],[$P$2,9,1],[$P$3,3,2],[$P$4,6,3],[$P$5,4,4]]$

Solve the above problem using SJF Non Preemptive and FCFS method also.