Question $1$: Explain briefly

a$)$ Is Prim a greedy algorithm? Why or why not?

b$)$ An elementary data structure is used in BFS$.$ Which one, how is it used?

c$)"$In an unweighted graph where the distance between any two vertices is at most T$,$ any

BFS tree has depth at most T$,$ but a DFS tree might have larger depth." Is the statement

true, why or why not?

d$)$ Throughout the entire execution of a breadth$-$first search, how much time is spent adding

and removing data to the data structure? Why?

e$)$ Explain why the running time of our topological sorting algorithm is what it is$.$

f$)$ What is the running time of the most deterministic algorithm you know for finding the

shortest path between two vertices in a directed graph, where the weights of all edges are

equal? $($Include the name of the algorithm$)$