Consider the following algorithm called Mystery. It calls a $($recursive$)$ helper algorithm

called anotherMystery.

a$.$ Trace what the algorithm does on the graph with the following adjacency matrix $($for

vertices $0,1,2,3,4,$ and $5)$ by showing what the labels are for each vertex and the value

in the variable count after each time a vertex has its label changed or when the value of

count changes. Briefly explain in words to clarify what is happening in your trace.

$\left[\begin{array}{cccccc}0& 0& 1& 0& 0& 1\\ 0& 0& 0& 0& 1& 0\\ 1& 0& 0& 0& 0& 1\\ 0& 0& 0& 0& 0& 0\\ 0& 1& 0& 0& 0& 0\\ 1& 0& 1& 0& 0& 0\end{array}\right]$

b$.$ What problem does the algorithm solve? That is$,$ what is an appropriate description of

its output $($what should we replace the $???$ above with$)?$

c$.$ Now suppose the input to the algorithm is a directed graph $G=(V,E).$ Is the

description you gave for part b still accurate? If so$,$ explain why. If not, provide a directed

graph for which the output of Mystery does not correspond to the description from part b$.$