Make sure to read carefully. You may write procedures in pseudocode or in any programming language the TA$$s know. Procedures can use $$helpers$.$ An$$adjacency structure$$is what Cormen mistakenly calls an$$adjacency list$$on page$550.$

$1.(15$ points.$)$ Suppose that$$G$$is a directed graph. It has an adjacency structure$$G$.$Adj,$$a set of edges$$G$.$E$,$and a set of vertexes$$G$.$V$.$Each vertex$$v$$G$.$V$$has an attribute$$v$.$mark$\{$TRUE$,$FALSE$\}.$ It has no other attributes! In particular, it has no$$color$,$ d$,$ f$,$or$$$$attributes like Cormen$$s vertexes do$.$

A vertex$$v$$G$.$V$$is an$$origin vertex$$in$$G$$if there is exactly one path from$$v$$to every other vertex in$$G$.$V$.$ The word$$origin$$is meant to suggest that every vertex in$$G$$is reachable starting from$$v$.$Don$$t bother looking for$$origin vertex$$online: the only hits you will get are irrelevant to this question: they deal with parabolas from high$-$school algebra.

Write a procedure IS$-$ORIGIN$($G$,$u$)$ that returns$$TRUE$$if the vertex$$u$$is an origin in the graph$$G$,$and returns$$FALSE$$otherwise$.$ Your procedure must always terminate, even if$$G$$has cycles or self edges. You will lose many points if it uses vertex attributes other than$$mark