Suppose you use the brute force (unimproved) algorithm to search for a Hamiltonian circuit in the graph shown here. E, a. How many links would such a circuit have? b. How many different paths would this algorithm examine? c. If this algorithm is run on a computer where it takes 0.0001 seconds to examine a single path, what is the total time required to examine all paths? d. On the same computer, what is the approximate total time required to examine all paths in a graph with 12 nodes, each of which has four choices for the next node?