$9.$ Consider the following algorithm for solving the $2-$process Critical Section Problem. Does the algorithm satisfy:

a$)$ Mutual Exclusion?

b$)$ Progress?

c$)$ Give an example where either $($a$)$ or $($b$)$ is not satisfied. $[2+2+5=9]$

Shared variables:

boolean flag$[2]$;

$/*$ initially flag $[0]=$ flag $[1]=$ false $*/$

flag $[$i$]=$ true $$ Pi ready to enter its critical section Process Pi

do $\{$

flag$[$i$]=$ true;$4$

$//$ Enter critical section

flag $[$i$]=$ false;

$//$ remainder section

$\}$ while $(1)$;