Q# 1: In a directed graph, we say that v can reach u if there is a directed path from v to u. A graph is strongly connected if for every pair u, v V , both v can reach u and u can reach v. Give an algorithm that checks if a directed graph is strongly connected.

Q# 2: Let the vertices of a directed graph be 1, 2, . . . n. Give an algorithm that finds for every vertex j the minimum i so that j can reach i.

Q# 3: Given an undirected graph, give an algorithm that returns the shortest simple cycle in the graph.