In Lecture $17,$ we saw a magic trick that can turn a BFS algorithm into a DFS algorithm

by simply replacing the queue with a stack. But I mentioned that this magic trick does not

work for all BFS algorithms. In this problem, we will see why.

Below is the BFS algorithm from Lecture $16,$ but with the queue replaced by a stack

attempting to make it into a DFS$.$ Find a counterexmaple, i$.$e$.$ construct a graph $G=$

$(V,E)($can be either directed or undirected$),$ such that for some vertex $sinV,$ running

$DFS-$VISIT$(G,s)$ does not correctly give you a DFS tree. The issue is with the sequence

of vertices that you visit, so you may safely ignore the teal$-$colored lines for the distances.

You should specify the graph $G($drawing it out is fine$)$ and the vertex $s$ that you run

DFS on$,$ along with a quick explanation of what goes wrong with the $($incorrect$)$ DFS tree

it produces.