Consider the following graph: 5 12 a 8 7 d 11 3 b g 10 a) Run Prim's algorithm on the graph, beginning at node a. Let F = 0, Y = {a}. The set F represent the set containing the minimum spanning tree at the conclusion of the algorithm. The set Y represent the set of vertices selected by the algorithm, containing all vertices of the graph at the conclusion of the algorithm. In your answer, trace the algorithm by rewriting the sets F and Y after each change. b) Report the path from a to e in the Minimum Spanning Tree output by Prim's algorithm.