2. (20 pts) Professor Snape gives you the following unweighted graph and asks you to construct a weight function w on the edges, using positive integer weights only, such that the following conditions are true regarding minimum spanning trees and single- source shortest path trees:

The MST is distinct from any of the seven SSSP trees. The order in which Jarn ??k/Prims algorithm adds the safe edges is different from the order in which Kruskals algorithm adds them.

Boruvkas algorithm takes at least two rounds to construct the MST.

Justify your solution by (i) giving the edges weights, (ii) showing the corresponding MST and all the SSSP trees, and (iii) giving the order in which edges are added by each of the three algorithms. (For Borukas algorithm, be sure to denote which edges are added simultaneously in a single round.)