4. Consider the following undirected, weighted graph (seen previously in #3): A 3 B 1 C 2 7 Edges Weight 3 10 12 Order vertices marked as known (done): 1) Neighbors of A D 2 E 2 Step through Prim's algorithm to calculate a minimum spanning tree, starting from vertex A. Show the edge coordinates and their corresponding weights. Specify the weight of the MST and also draw the MST. F
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- Given N cities represented as vertices V₁, V2, un on an undirected graph (i.e., each edge can be traversed in both directions). The graph is fully-connected where the edge eij connecting any two vertices vį and vj is the straight-line distance between these two cities. We want to search for the shortest path from v₁ (the source) to VN (the destination). ... Assume that all edges have different values, and €₁,7 has the largest value among the edges. That is, the source and destination have the largest straight-line distance. Compare the lists of explored vertices when we run the uniform-cost search and the A* search for this problem. Hint: The straight-line distance is the shortest path between any two cities. If you do not know how to start, try to run the algorithms by hand on some small cases first; but remember to make sure your graphs satisfy the conditions in the question.Given the following graph, A C 3 1 E 4 В F 7 D 5 What is the next edge and vertex(s) to be included in the solution if a. we are using Prim's algorithm to find a minimum spanning tree and we have started with vertex E? Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if b. we are using Kruskal's algorithm to find a minimum spanning tree Edge: Vertex(s): What is the next edge and vertex(s) to be included in the solution if c. we are using Dijkstra's shortest path algorithm to find shortest paths and we have started with vertex E, with C and F already included in the shortest path tree? Edge: Vertex(s):Computer science question help
- Mark Zuckerberg, the CEO of Facebook, has hired you to lead the Facebook Algorithms Group. He has asked you to use various graph algorithms to analyze the world's largest social network. The Facebook Graph has 2.8 billion vertices, with each vertex being a Facebook user. Two vertices are connected provided those two users are "friends". The first decision you need to make is how you want to model the Facebook graph. Determine whether you should use an adjacency-list representation or an adjacency-matrix representation.Consider the following edge-weighted digraph with 8 vertices and 13 edges. V->W weight A->E 1 A->B B->C C->F 4 C->D D->G F->E 39 23 F->B 26 F->A 16 G->F G->C 40 34 H->D 95 H->G 17 Here is a graphical representation of the same edge-weighted digraph: (A) -3---->(B) -39-->(D) 16 95 (E)- -23- (F). 40 (G) (H) Suppose that you run the Bellman-Ford algorithm to compute the shortest paths from H to every other vertex. What is the distTo[] array immediately after the end of three passes of the algorithm (pass 1, 2, and 3)? Each pass consists of relaxing the 13 edges in the order given above. Here is the distTo[] array before the beginning of pass 1: v A B CDE F H. distTo(v] Answer Your answer should be a sequence of 8 integers, separated by whitespace,Consider the following edge-weighted graph with 10 vertices and 17 edges. V-w weight A-B 8. F-A 6. G-B 15 B-F C-B D-C 16 C-G 12 C-H C-I D-I 17 D-E 11 I-E 13 J-E 10 G-F 9. H-G I-H 14 1 I-J Here is a graphical representation of the same edge-weighted graph: (A) -8- (C)------16----- (D)---- --11-----(E) 7|\ 13 10 (F) (G) Give the sequence of edges in the MST in the order that Prim's algorithm adds them to the MST, when starting Prim's algorithm from vertex H. To specify an edge, use its weight.