We can trivially generalize steps in Dijksras and Prims algorithms to a directed graph, by only considering neighbors of a newly added node that can be reached by following edges in the direction from the newly added node to the neighbors (you would get this automatically if the adjacency lists of a node only include outgoing edges). Find:

a. The Dijkstras spanning tree from node A (using Dijkstras algorithm). Show the order in which you add nodes into the tree as it is being built, and draw the resulting tree.

b. The Prims spanning tree from node A (using Prims algorithm). Show the order in which you add nodes into the tree as it is being built, and draw the resulting tree.

c.Does the Dijkstras spanning tree built in the previous step represent a shortest-path spanning tree? Does the Prims spanning tree of the previous step represent a minimum spanning tree?

F (E 1 (G ) 3 (C 7 B D) 2 (A