Let G=(V, E) be a simple directed graph in which every vertex u has some (real-valued) fine, which we denote by fine(u). For each vertex u, let MinFine(u) be the minimum fine that is reachable from vertex u in graph G. In other words, MinFine(u) = min (fine(r): z E reach(u)}, where reach(u) is the set of vertices v EV reachable by a path in G from vertex u (that is, such that G has a (u, v)-path). (i) Show that if two vertices u, v V are in the same strongly connected component in G, then MinFine(u) = MinFine (v). (ii) Design an O(n + m)-time algorithm that for any directed acyclic graph G determines the minimum fine from each vertex in G (that is, computes MinFine(u) for all vertices u EV). Explain your answer, prove correctness of your algorithm and give arguments about its running time. (iii) Use (1) and (ii) to design an O(n+m)-time algorithm that for any simple directed graph G (not necessarily acyclic) determines the minimum fine reachable from each vertex in G (that is, computes MinFine(u) for all vertices u V). Explain your answer, prove correctness of your algorithm and give arguments about its running time.