$5.$ findCycle: Finding a cycle in a directed graph using depth$-$first search $($hard$)(25$ points$)$

A directed graph is a graph where edges are directional; that is$,$ edges $($p$,$q$)$ and $($q$,$p$)$ are distinct. An important class of directed graphs are directed acyclic graphs $($DAGs$),$ which have broad applications in programming languages and compilers. A DAG is any directed graph with no cycles. For example, this is a directed graph: The above graph is not a DAG because it contains cycles.