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Exercise 1 - Hash tables (30 pts) a) Insert the following keys in a hash table of size 13: 38, 12, 0, 26, 17, 52, 61. You may use the hash function h(x) = 7 - x mod 7 to resolve collisions. b) What is the overall running time of your algorithm? Does sorting the elements first improve it? Exercise 2 MST (30 pts) Prims algorithm allows us to find the minimum spanning tree in a weighted graph. It is identical to Kruskal's one (except for the update rule when processing a vertex of the graph). a) Apply Prim's algorithm to find the MST for the following graph. 5 6 7 5 3 2 6 5 b) Explain briefly how you compute its asymptotic running time. c) Which programming strategy does it use