Remarks: In al algorithm, always explain how and why they work. ALWAYS, analyze the complexity of your algorithms. Prove that it works. In all algorithms, always try to get the fasiesi possible. correxi algorithm with slow running inne may noi: ei mil credit. Iu all data structures, try to minimize as much as possible the running time of any operation. . Question 4: A tournament graph is a directed graph that has all edges uv, except v or v->u (note that the number of edges is (2) that we either have the edge u Indeed its as if we have n teams, and every pair of two teams plays one basketball game. If u lost to v, the tournament will have the edge u H> v. Clearly what we get is a tournament graph. Show that every tournament graph contains am Hamiltonian path. (Hint: Induction will make the answer simple). Give an algorithm that finds an Hamiltonian path in a tournament