ne N. Consider a directed acyclic graph G = (N,E) with a source node m = N and target node P2.1. Provide an algorithm that computes the number of paths starting at m and ending at n. P2.2. We say that the directed acyclic graph G has a bottleneck if there is a node b, distinct from source m and target n, such that all paths from m to n go through node b. Write an algorithm that returns true if and only if G has such a bottleneck. You may assume that there is at-least one path from m to n. For each question, explain why your algorithm is correct, what the complexity of your algorithm is, and which graph representation you use.