Computer Science: An Overview (13th Edition) (What's New in Computer Science)
13th Edition
ISBN: 9780134875460
Author: Glenn Brookshear, Dennis Brylow
Publisher: PEARSON
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Chapter 11.3, Problem 6QE
Program Plan Intro
Heuristic system:
The heuristic system considers all the immediate possible conditions that may lead to a solution for the problem. The system proceeds in the same manner until all the possible conditions are achieved. The heuristic system may require a large amount of work, but ultimately it approaches towards a solution. The solution is one of the conditions achieved at the last. The conditions achieved at last may be in a large number. It guarantees to have a solution among many conditions achieved in the end.
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11. For the given graph below, use the depth-first search algorithm to visit the
vertices and write the sequence of the visit. Start from the vertex "A". At any
given vertex, you will visit first the unexplored vertex that has least alphabetical
order.
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E
F
Answer the sequence of visiting the vertices: -_
a) Given a depth-first search tree T, the set of edges in T are referred to as "tree edges" while those not in T are
referred to as "back edges". Modify the implementation of the Depth-First Search algorithm to print out the
set of tree edges and the set of back edges for the following graph.
1(0 1 1 0 0 1 0)
210 100 0 0
31 10 10 1
4 0 0
1
0 0 0 0
50 0 0 00
1
1
1 0 1
70 0 1 0 1 1 0
6 1 0
0 0
4. Please apply Kruskal's spanning tree algorithm in the graph below and find the minimum spanning tree
(MST). Edge weights are in the adjacency matrix table. (you can list the edges in MST or draw the tree below)
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b
a
e
h
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The adjacency matrix for the undirected weighted graph is mentioned below:
a
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h
a
4
8
4
8
11
8.
7
4
2
d
7
14
e
9.
10
f
4
14
10
2
1
6.
8.
11
1
7
7
Chapter 11 Solutions
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Ch. 11.1 - Prob. 1QECh. 11.1 - Prob. 2QECh. 11.1 - Prob. 3QECh. 11.1 - Prob. 4QECh. 11.1 - Prob. 5QECh. 11.2 - Prob. 1QECh. 11.2 - Prob. 2QECh. 11.2 - Prob. 3QECh. 11.2 - Prob. 4QECh. 11.2 - Identify the ambiguities involved in translating...
Ch. 11.2 - Prob. 6QECh. 11.2 - Prob. 7QECh. 11.3 - Prob. 1QECh. 11.3 - Prob. 2QECh. 11.3 - Prob. 3QECh. 11.3 - Prob. 4QECh. 11.3 - Prob. 5QECh. 11.3 - Prob. 6QECh. 11.3 - Prob. 7QECh. 11.3 - Prob. 8QECh. 11.3 - Prob. 9QECh. 11.4 - Prob. 1QECh. 11.4 - Prob. 2QECh. 11.4 - Prob. 3QECh. 11.4 - Prob. 4QECh. 11.4 - Prob. 5QECh. 11.5 - Prob. 1QECh. 11.5 - Prob. 2QECh. 11.5 - Prob. 3QECh. 11.6 - Prob. 1QECh. 11.6 - Prob. 2QECh. 11.6 - Prob. 3QECh. 11.7 - Prob. 1QECh. 11.7 - Prob. 2QECh. 11.7 - Prob. 3QECh. 11 - Prob. 1CRPCh. 11 - Prob. 2CRPCh. 11 - Identify each of the following responses as being...Ch. 11 - Prob. 4CRPCh. 11 - Prob. 5CRPCh. 11 - Prob. 6CRPCh. 11 - Which of the following activities do you expect to...Ch. 11 - Prob. 8CRPCh. 11 - Prob. 9CRPCh. 11 - Prob. 10CRPCh. 11 - Prob. 11CRPCh. 11 - Prob. 12CRPCh. 11 - Prob. 13CRPCh. 11 - Prob. 14CRPCh. 11 - Prob. 15CRPCh. 11 - Prob. 16CRPCh. 11 - Prob. 17CRPCh. 11 - Prob. 18CRPCh. 11 - Give an example in which the closed-world...Ch. 11 - Prob. 20CRPCh. 11 - Prob. 21CRPCh. 11 - Prob. 22CRPCh. 11 - Prob. 23CRPCh. 11 - Prob. 24CRPCh. 11 - Prob. 25CRPCh. 11 - Prob. 26CRPCh. 11 - Prob. 27CRPCh. 11 - Prob. 28CRPCh. 11 - Prob. 29CRPCh. 11 - Prob. 30CRPCh. 11 - Prob. 31CRPCh. 11 - Prob. 32CRPCh. 11 - Prob. 33CRPCh. 11 - What heuristic do you use when searching for a...Ch. 11 - Prob. 35CRPCh. 11 - Prob. 36CRPCh. 11 - Prob. 37CRPCh. 11 - Prob. 38CRPCh. 11 - Suppose your job is to supervise the loading of...Ch. 11 - Prob. 40CRPCh. 11 - Prob. 41CRPCh. 11 - Prob. 42CRPCh. 11 - Prob. 43CRPCh. 11 - Prob. 44CRPCh. 11 - Prob. 45CRPCh. 11 - Draw a diagram similar to Figure 11.5 representing...Ch. 11 - Prob. 47CRPCh. 11 - Prob. 48CRPCh. 11 - Prob. 49CRPCh. 11 - Prob. 50CRPCh. 11 - Prob. 51CRPCh. 11 - Prob. 52CRPCh. 11 - Prob. 53CRPCh. 11 - Prob. 54CRPCh. 11 - Prob. 1SICh. 11 - Prob. 2SICh. 11 - Prob. 3SICh. 11 - Prob. 4SICh. 11 - Prob. 5SICh. 11 - Prob. 6SICh. 11 - Prob. 7SICh. 11 - Prob. 8SICh. 11 - Prob. 9SICh. 11 - Prob. 10SICh. 11 - Prob. 11SICh. 11 - Prob. 12SICh. 11 - A GPS in an automobile provides a friendly voice...Ch. 11 - Prob. 14SI
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- A. Use Prim’s algorithm starting at node A to compute the Minimum Spanning Tree (MST) of the following graph. In particular, write down the edges of the MST in the order in which Prim’s algorithm adds them to the MST. Use the format (node1; node2) to denote an edge B. For the same graph as above, write down the edges of the MST in the order in which Kruskal’s algorithm adds them to the MST. NB: Graph in imagearrow_forward1. Unreachable Nodes You have been given an undirected graph consisting of N nodes and Medges. The nodes in this graph are enumerated from 1 to N. The graph can consist of self-loops as well as multiple edges. This graph consists of a special node called the head node. You need to consider this and the entry point of this graph. You need to find the number of nodes that are unreachable from this head node. Create a function unreachableNodesCount (N, M, ListofEdges, HeadNode) where N is the number of nodes, M is the number of edges, List0fEdges contains list of edges in the graph and HeadNode is a special node which is the entry point of this graph. The function will return the number of nodes that are unreachable from the head node. Note: You will need to use N, M and List of Edges to first create the graph, as well as a search function to define the unreachable nodes count. >>>N = 10 >>> M = 10 >>> ListofEdges [(8, 1), (8, 3), (7, 4), (7, 5), (2, 6), (10, 7), (2, 8), (10, 9), (2, 10),…arrow_forwardCode:algorithm LeveledGraph (G, s,t) pre-cond: G is a weighted directed layered graph, and s and t are nodes. post-cond: optSol is a path with minimum total weight from s tot, and optCost is its weight, and optNum is the number of possible optimal solutions.arrow_forward
- 4. a. Use Prim's algorithm starting at node A to compute the Minimum Spanning Tree (MST) of the following graph. In particular, write down the edges of the MST in the order in which Prim's algorithm adds them to the MST. Use the format (nodel; node2) to denote an edge. E 20 11 13 15 14 10 F 12 B b. For the same graph as above, write down the edges of the MST in the order in which Kruskal's algorithm adds them to the MST.arrow_forwardGraph Transversal Simulation: For this graph write down the order of vertices encountered in a breadth-first search starting from vertex A. Break ties by picking the vertices in alphabetical order (for example, A before Z)arrow_forwardDiscussion:1. Depth-first search (DFS) is a technique that is used to traverse a tree or a graph.DSF technique starts with a root node and then traverses the adjacent nodes ofthe root node by going deeper into the graph. In the DFS technique, the nodes aretraversed depth-wise until there are no more children to explore.- Once we reach the leaf node (no more child nodes), the DFS backtracks andstarts with other nodes and carries out traversal n a similar manner. DFStechnique uses a stack data structure to store the nodes that are beingtraversed. DFS Technique (Depth-First Traversal)o Following is the algorithm for the DFS technique.o Algorithm:1. Start with the root node and insert it into the stack2. Pop the item from the stack and insert into the ‘visited’ list3. For the node marked as ‘visited’ (or in visited list), add the adjacent nodesof this node that are not yet marked visited to the stack.4. Repeat steps 2 and 3 until the stack is empty.arrow_forward
- Question 18 Consider the graph below. Use Prim's algorithm to find a minimal spanning tree of the graph rooted in vertex A. Note: enter your answer as a set of edges {E1, E2, ...} and write each edge as a pair of nodes between parentheses separate by a comma and one blank space e.g. (A, B) 6. D 3 4 1 F 4 C Barrow_forwardalgorithm ShortestPath (G, s) pre-cond: G is a (directed or undirected) graph, and s is one of its nodes. post-cond: π specifies a shortest path from s to each node of G, and d specifiestheir lengths.arrow_forwardalgorithm GenericSearch (G, s) pre-cond: G is a (directed or undirected) graph, and s is one of its nodes. post-cond: The output consists of all the nodes u that are reachable by a path in G from s.arrow_forward
- The Graph Data Structure is made up of nodes and edges. (A Tree Data Structure is a special kind of a Graph Data Structure). A Graph may be represented by an Adjacency Matrix or an Adjacency List. Through this exercise, you should be able to have a better grasp the Adjacency Matrix concept. You are expected to read about the Adjacency Matrix concept as well as the Adjacency List concept. Suppose the vertices A, B, C, D, E, F, G and H of a Graph are mapped to row and column indices(0,1,2,3,4,5,6,and 7) of a matrix (i.e. 2-dimensional array) as shown in the following table. Vertex of Graph Index in the 2-D Array Adjacency Matrix Representation of Graph A B 2 F 6. H 7 Suppose further, that the following is an Adjacency Matrix representing the Graph. 3 4 5. 6. 7 0. 1 1 1 1 01 1 01 1. 3 14 1 1 1 6. 1 Exercise: Show/Draw the Graph that is represented by the above Adjacency matrix. Upload the document that contains your result. (Filename: AdjacencyMatrixExercise.pdf) Notes: -The nodes of the…arrow_forward4-Clique Problem The clique problem is to find cliques in a graph. A clique is a set of vertices that are all adjacent - connected - to each other. A 4-clique is a set of 4 vertices that are all connected to each other. So in this example of the 4-Clique Problem, we have a 7-vertex graph. A brute-force algorithm has searched every possible combination of 4 vertices and found a set that forms a clique: https://en.wikipedia.org/wiki/Clique_problem You should read the Wikipedia page for the Clique Problem (and then read wider if need be) if you need to understand more about it. Note that the Clique Problem is NP-Complete and therefore when the graph size is large a deterministic search is impractical. That makes it an ideal candidate for an evolutionary search. For this assignment you must suppose that you have been tasked to implement the 4-clique problem as an evolutionary algorithm for any graph with any number of vertices (an n-vertex graph). The algorithm succeeds if it finds a…arrow_forwardb) Apply an algorithm to find the minimum spanning tree. To solve this problem, you need to transfer the unweighted graph into weighted graph and you can do it by using your mobile number (11 digits). Just assign the digits sequentially (left to right) to the edges of binary tree segment (means black color edges). And for rest of the edges, you may write 1 as their weights.arrow_forward
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