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Consider the weighted, directed graph containing the following vertices and edges. (Weights are in the parentheses.) Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)} a. Starting at vertex C, determine the shortest path tree using Dijkstra b. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not? c. Starting at vertex C, determine the minimum spanning tree using Prim. d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?

Consider the weighted, directed graph containing the following vertices and edges. (Weights are in the parentheses.) Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)} a. Starting at vertex C, determine the shortest path tree using Dijkstra b. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not? c. Starting at vertex C, determine the minimum spanning tree using Prim. d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?

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1. Consider the weighted, directed graph containing the following vertices and edges.
(Weights are in the parentheses.)
Vertices: {A, B, C, D} Edges: {AB(5), BC(3), CA(4), AD(2), DA(4), CB(3)}
a. Starting at vertex C, determine the shortest path tree using Dijkstra
b. If you were to apply Floyd-Warshall’s algorithm to this tree, would it include the shortest path tree you found using Dijkstra? Why or why not?
c. Starting at vertex C, determine the minimum spanning tree using Prim.
d. Would Kruskal’s algorithm always result in the same MST as Prim’s? Why or why not?

 

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