2. Long paths in DAGs * Give a polynomial-time algorithm for computing a longest path in a DAG (directed acyclic graph). Next, given a polynomial-time algorithm that, given a DAG G and an integer k, computes the number of paths in G that are of length at least k. 3. Long paths in a graph * Consider the following problem: We are given a graph G and want to compute a longest path in G. Suggest a polynomial-time algorithm for this problem, and then give an example on which the algorithm fails in computing the correct answer. Conclude that the algorithm does not work. In fact, there is no known polynomial-time algorithm for this problem. Compare and contrast the two problems: finding a longest path in a DAG versus finding a longest path in a general graph