15. The shortest 3-vertex path problem is: input: an undirected graph G=(V,E) output: a list P of 3 vertices corresponding to a path in G of minimum length Which pattern is most appropriate for this problem: proper exhaustive search, or exhaustive optimization? Justify why? 16. For the problem above, what is the data type of one candidate solution? 17. For the problem above, design an algorithm for this problem using the pattern you picked in the previous question. Write pseudocode for your algorithm below. If you write multiple drafts, circle your final draft. You are welcome to use any of the following enumeration algorithms, without restating their pseudocode or proving their efficiency. algorithm time complexity Subsets (powerset) O(n.2an) permutations 0n:n!) 15. The shortest 3-vertex path problem is: input: an undirected graph G=(V,E) output: a list P of 3 vertices corresponding to a path in G of minimum length Which pattern is most appropriate for this problem: proper exhaustive search, or exhaustive optimization? Justify why? 16. For the problem above, what is the data type of one candidate solution? 17. For the problem above, design an algorithm for this problem using the pattern you picked in the previous question. Write pseudocode for your algorithm below. If you write multiple drafts, circle your final draft. You are welcome to use any of the following enumeration algorithms, without restating their pseudocode or proving their efficiency. algorithm time complexity Subsets (powerset) O(n.2an) permutations 0n:n!)