(25 Points) Let G = (V, E) be a directed graph in which each vertex u E V is labeled with a unique integer L (u) from the set {1, 2, ...,V]}. For each vertex u EV, let R(u) = {v EV: Undv} be the set of vertices that are reachable from u. Define min (u) to be the vertex in R(u) whose label is minimum, i.e., min (u) is the vertex v such that L (v) = min{L (w): WE R(u)}. Give an O (V + E)-time algorithm that computes min (u) for all vertices u EV. (25 Points) Let G = (V, E) be a directed graph in which each vertex u E V is labeled with a unique integer L (u) from the set {1, 2, ...,V]}. For each vertex u EV, let R(u) = {v EV: Undv} be the set of vertices that are reachable from u. Define min (u) to be the vertex in R(u) whose label is minimum, i.e., min (u) is the vertex v such that L (v) = min{L (w): WE R(u)}. Give an O (V + E)-time algorithm that computes min (u) for all vertices u EV