A directed graph is said to have the SC$-$property if for every pair of vertices

$($u$,$ v$)$ there is atmost one simple path from u to v$.$

a$.(12$ pts$)$ Let G $=($V$,$ E$)$ be a given directed graph. Given u in V $,$ design an algorithm to

decide if there is atmost one simple path from u to every other v in V $\backslash \{$u$\}.$ Analyze the time

complexity of your algorithm.

b$.($Bonus question, $3$ pts$)$ Give an O$(|$V $|2+|$V $||$E$|)-$time algorithm to check if a given directed

graph G has the SC$-$property