Consider the following directed graph $G$ given by adjacency lists $($first column indi$-$

cates the vertex, the second column lists its outgoing edges as a list$)$:

$($a$)(4$ pts$.)$ Perform Depth$-$First Search on this graph starting from vertex $0.$ Indi$-$

cate the stack after each addition$/$removal$,$ the order in which the vertices are

marked $($start every new DFS from the first unmarked vertex$).$

$($b$)(4$ pts$.)$ Find the preorder, the postorder, and the reverse postorder of the

vertices corresponding to this search. Which of these give you a topological

order of the vertices, if any?