) Using the same diagram in Figure 1, apply Prim's algorithm to find the minimum spanning tree. Assume vertex B as the source.
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- 7. Start from vertex A, use Prim's algorithm to find a minimum spanning tree (MST) for the following weighted graph: F 3 6 E A 5 2 7 D B 2 3 C Show the weight of the MST, the sequences of the edges added to the MST during the construction and draw the MST.Given: 13-Node Graph O 75 AD 118 DZ T 140 D to B-242 F to B-176 L to B-244 M to B-241 O to B-380 P to B - 100 RV to B - 193 S to B-253 T to B-329 Z to B-374 70 D 151 OM S 120 80 Straight-Line Distance to Node B A to B - 366 B to B-0 C to B-160 8 RV 97 146 C 138 F P Problem: Generate the A* from Node A to Node B Solve the A* from Node A to Node B. 101 211 B1. Draw a tree with 14 vertices 2. Draw a directed acyclic graph with 6 vertices and 14 edges 3. Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? –Adjacency Matrix –Adjacency List –Edge List
- 3. Find the shortest path from c to fusing the Dijkstra's algorithm in graph K3. Fill in the table below. Number 1 in the table is given as an example. 5 а 3 2 4 5 5 b 2 3 d K3 Shortest distance from c 1. 0 Previous Vertex Vertex Status 2. d 13. 3. 5. 4. 7. 6. 10. b 18. 8. 11. e 9. 14. 12. 16. a 21. 15. 17. 19. 20. The shortest path from c to fis: 3.50. Use the Breadth-First Spanning Tree Search Algorithm to find a spanning tree of K,. Start from vertex h. Remember, we start with vertex h being labeled 0. b K6 a. Vertices that should be labeled as step 1: b. Vertices that should be labeled as step 2: c. Vertices that should be labeled as step 3: d. Edges that need to be removed to get a spanning tree:Apply Dijkstra's Algorithm using all the Data Structures A, V, Parent and recreate the paths from the source (vertex labeled '1'). 3 2 2
- 3. From the graph above determine the vertex sequence of the shortest path connecting the following pairs of vertex and give each length: a. V & W b. U & Y c. U & X d. S & V e. S & Z 4. For each pair of vertex in no. 3 give the vertex sequence of the longest path connecting them that repeat no edges. Is there a longest path connecting them?Given Prim's pseudocode algorithm used as voraz algorithm (Figure 1) Where (pi) are the ancestors of the vertex in question and Q are the vertices that can be considered for expansion. Find the minimum generation tree for the graph in Figure 2 To carry out the exercise, the data structure shown in the second Table will be used. (First Table: PRIM data structure) Vertex a b c d e f g h i weight 0 inf. inf. inf. inf. inf. inf. inf. inf. pi null null null null null null null null null Q X X X X X X X X X * inf. = infinity symbol In an initial stage, the vertex a is selected and therefore we start with a weight of 0. Then, the neighbors are updated (for example, the neighbors of a are b and h). They will only be updated if the update is a lower weight than an already known one. For example, from vertex a it expands to vertex b and h leaving the table as shown below: (Second Table: First iteration) Vertex a b c d e f g h i weight 0 4 inf. inf. inf. inf. inf. 8 inf. pi…Given PRIM's pseudocode algorithm used as voraz algorithm (Figure 1) Where (pi) are the ancestors of the vertex in question and Q are the vertices that can be considered for expansion. Find the minimum generation tree for the graph in Figure 2 To carry out the exercise, the data structure shown in the second Table will be used. (First Table: PRIM data structure) Vertex a b c d e f g h i weight 0 inf. inf. inf. inf. inf. inf. inf. inf. pi null null null null null null null null null Q X X X X X X X X X * inf. = infinity symbol In an initial stage, the vertex a is selected and therefore we start with a weight of 0. Then, the neighbors are updated (for example, the neighbors of a are b and h). They will only be updated if the update is a lower weight than an already known one. For example, from vertex a it expands to vertex b and h leaving the table as shown below: (Second Table: First iteration) Vertex a b c d e f g h i weight 0 4 inf. inf. inf. inf. inf. 8 inf. pi…
- 8. For the weighted graph depicted below apply Prim's algorithm to find a minimal spanning tree. Show the steps of the algorithm, draw the resulting spanning tree and determine its total weight. 1 6 11 b d 10 8 7 3 13 a 20 24 11 fDraw a tree with 14 vertices Draw a directed acyclic graph with 6 vertices and 14 edges Suppose that your computer only has enough memory to store 40000 entries. Which best graph data structure(s) – you can choose more than 1 -- should you use to store a simple undirected graph with 200 vertices, 19900 edges, and the existence of edge(u,v) is frequently asked? - Adjacency Matrix - Adjacency List - Edge ListQ1 Q2 a. b. How many spanning trees does the following graph have? Consider the following graph and answer the corresponding questions с 142 171 B D 92 250 140 261 134 81 163 4 63 E Provide the MST generated using Prim's algorithm showing how the order of which edges were added in step by step Provide the MST generated using Kruskal's algorithm showing the order with which edges were added in