Give the execution trace of running Prim's algorithm on the following graph starting from vertex a, where any ties are broken by alphabetical order. That is, for each step of the algorithm state the current (partial) spanning tree constructed thus far, the current vertex being looked at, and the vertices whose parameters val and pred are updated and what they are updated to that round. S 1 a 3 2 7 28, d. 8 1 10. (10pts) Previously we considered the problem of finding minimum spanning trees in a graph. It is equally valid to find maximum spanning trees. Give (the pseudo-code of) an algorithm for finding the maximum spanning tree in graph.