Carry out the Prim MST algorithm on the weighted undirected graph below. Use A as the source vertex. The algorithm data structures are described on pp. 397-403 of the text. 7,07 2.0 3.0 14.1 \ 50 0 20 75.0 8.0 0 1. 0 1. (10 points) Show the priority queue table just before each edge is added, then indicate which edge is chosen from that table to be a tree edge, and continue with the updated table in a new diagram, and the next chosen edge, and so on, until the tree is complete. Your new diagram for each step should show all the data for fringe vertices and for vertices whose status changed. To save time and clutter you do not need to repeat data for vertices in intermediate diagrams that did not change since the prior diagram. But make the final diagram complete. 2. (5 points) How does one use the final table to find the total weight of the minimum spanning tree that was found? 3. (5 points) Illustrate (partly) how the MST that was found obeys the Minimum Spanning Tree Property using the heaviest edge not in the MST and the lightest edge not in the MST