$(10$ points$)$ Consider the following problem:

Given a directed graph G$,$ determine if there exists a vertex v such that for all vertices uinV,

there exists a path from v to u$|$V$|$ and $|$E$|$ ; a directed graph with vertex set V and edge set E SCC algorithm on G$.$

if cc$==1$ then

return TRUE

else

return FALSE

$($b$)$ ; a directed graph with vertex set V and edge set E G$.$

Identify h as the vertex with the highest post number from the previous step.

Run explore on G starting from h$.$

if all vertices are visited then

return TRUE

else

return FALSE