Solve subparts 7a,7b and 7c
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Solve subparts 7a,7b and 7c
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- 5. If the seventh digit of your student ID is an ODD digit, answer Question 5.(a). Otherwise, answer Question 5.(b) [for an EVEN digit]. G 2 12 7 B D (A 1 2 F 3 3 E 10 Fig. 3. Undirected Graph G for Question 5 a) Assume that the vertex A, B, C, D, E, F and G represent seven different places in your neighborhood and the weight of the edges represent the distance in km between these places. Your job is to compute the Minimum Spanning Tree covering the given graph. Explain your computational process in detail. b) Assume that the vertex A, B, C, D, E, F and G represent seven different places in your neighborhood and the weight of the edges represent the distance in km between these places. Your job is to compute the Shortest Path distance from A to other places. Explain your computational process in detail.PROBLEM 5 Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex A. Explain and justify each step as you add an edge to the tree. 2 A 5 E 6 4 7 в D 3 Figure 10: A uweighted graph shows 5 vertices, represented by circles, and 6 edges, represented by line segments. Vertices A, B, C, and D are placed at the corners of a rectangle, whereas verter E is at the center of the rectangle. The edges, A B, B D, A C, C D, A E, and E C, have the weights, 7, 3, 2, 4, 5, and 6, respectively.A B. D H Suppose you run the topological sort algorithm on the graph above starting at vertex C. Use the rule that when there is a choice of vertices for the algorithm to visit, it visits them in alphabetic order. Which vertex would end up first in the eventual topologically sorted order? Which would end up being second? Which would end up being third? Which would end up being fourth? Which would end up being fifth? Which would end up being sixth?
- Computer Science: Data Structures and Algorithm (C Programming) A strongly connected component (SCC) of a directed graph G(V,E) is a maximal set of vertices C⊆V suchthatforeverypairofverticesuandvinC,wehavebothu↝vandv↝u;that is, vertices u and v are reachable from each other.In the example graph given below, the sets of nodes a, b, e, c, d, f, g, and h each form a strongly connected component. Thus, the graph consists of 4 strongly connected components. (a) Breadth First Search (BFS) can be used in determining whether each node in a given directed graph is reachable by every other node. Give the pseudocode of an algorithm using BFS that determines whether a given directed graph is a single SCC. Also provide the explanation of your algorithm in plain English along with a runtime analysis. (b) Depth First Search (DFS) can be used to calculate strongly connected compo- nents in a graph. Give the pseudocode of an algorithm using DFS that calculates SCCs in a given directed graph. Also…3. a) How can you store the following graph in a computer memory? 5 3 1 3 3 0 2 -2 12 4 7 2 b) Determine the shortest path from vertex '0' to vertex '2' of the above-mentioned graph. c) Illustrate 'Depth First Search' for the above-mentioned graph.Objectives - Write a program to calculate minimum spanning tree using Kruskal's algorithm The graph below is from the Minimum Spanning Tree lecture. For vertices, you can use numbers instead of letters. Keep the edge weights the same, the result of your program should be 38. Vertices: A, B, C, D, E, F, G 1, 2, 3, 4, 5, 6, 7 10 6 8 8 10 7. 8 12 Sample Output Finding MST using Kruskal's Algorithm Edges of MST are 1 - 6 = 5 1 - 2 = 6 2 - 7 = 7 3 - 7 = 5 5 - 7 = 7 4 - 5 = 8 Weight of MST is 38
- 5 3 3 3 0 -2 12 4 7 1 2 2 b) Determine the shortest path from vertex '0' to vertex '2' of the above-mentioned graph. c) Illustrate 'Depth First Search for the above-mentioned graph.(9) An undirected weighted graph G is given below: a d 5 2 3 6 لها b 8 5 7 e 1 4 3 с 6 3 4 f 4 4 h 2 8 Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex a.Case Study 5 9 0 2 1 8 Figure 2 4 7 5 6 Problem: Most graph algorithms involve visiting each vertex in a systematic order. The two most common traversal algorithms are Breadth First Search (BFS) and Depth First Search (DFS). Implementation: Use the Graph above, (Figure 2) to answer the following questions. 1. What type of graph is shown in Figure 2? 2. Perform a Breath First Search (BSF) on the above Graph. (Figure 2). Show the necessary steps using the sample table below.
- 2. Use a deep-first search to find a spanning tree of the following graph starting from vertex а. (a) Write the list of the edges of the spanning tree in the order you add them. (b) Draw the minimal spanning tree.PROBLEM 5 Use Prim's algorithm to compute the minimum spanning tree for the weighted graph. Start the algorithm at vertex A. Explain and justify each step as you add an edge to the tree. 2 A 7 E 4 D 3 Figure 10: A weighted graph shows 5 vertices, represented by circles, and 6 edges, represented by line segments. Vertices A, B, C, and D are placed at the corners of a rectangle, whereas verter E is at the center of the rectangle. The edges, A B, B D, A C, C D, A E, and E C, have the weights, 7, 3, 2, 4, 5, and 6, respectively. B.Problem 2. Perform Breadth-First Search on the undirected graph shown in figure 2 (or show the order in which all the vertices will be discovered or visited). The starting vertex is 'A'. A B D E F G H