EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels
traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest
form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the
same color; this is called a vertex coloring. The chromatic number of a graph is the least
mumber of colors required to do a coloring of a graph.
Example
Here in this graph the chromatic number is 3 since we used 3 colors
The degree of a vertex v in a graph (without loops) is the number of edges at v. If
there are loops at v each loop contributes 2 to the valence of v.
A graph is connected if for any pair of vertices u and v one can get from u to v by
moving along the edges of the graph. Such routes that move along edges are known
by different names: edge progressions, paths, simple paths, walks, trails, circuits,
cycles, etc.
a. Write down the degree of the 16 vertices in the graph below:
14…
Programming with Python:
v Implement Depth First Search (Traversal)
v Implement Breadth First Traversal
For the implementation:
1. Create a directed graph with 10 Vertices
2. Add arbitrary edges among vertices to satisfy the directed graph
3. Run your program and show appropriate output (Traversal order)
4. Your implementation should be fully commented
Please, submit your source code and output (Screen Capture) too.
Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.Solve the above problem using adjacency list representation.
Chapter 8 Solutions
EBK DATA STRUCTURES AND ALGORITHMS IN C
Knowledge Booster
Similar questions
- 5. Icosian Game A century after Euler's discovery (see Problem 4), another famous puzzle-this one invented by the renowned Irish mathematician Sir William Hamilton (1805–1865)-was presented to the world under the name of the Icosian Game. The game's board was a circular wooden board on which the following graph was carved: Find a Hamiltonian circuit-a path that visits all the graph's vertices exactly once before returning to the starting vertex-for this graph.arrow_forwardIn graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. in its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring.", Wikipedia a) Apply your algorithm in the graph below. What is the accuracy ratio? b) Show that the performance ratio of your algorithm can go unbounded above or never at all.arrow_forwardWrite a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (6 Marks)(i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.arrow_forward
- In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem. Following is the problem statement: There are n people standing in a circle waiting to be executed. The counting out begins at some point (rear) in the circle and proceeds around the circle in a fixed direction. In each step, a certain number (k) of people are skipped and the next person is executed. The elimination proceeds around the circle (which is becoming smaller and smaller as the executed people are removed), until only the last person remains, who is given freedom. Given the total number of persons n and a number k which indicates that k-1 persons are skipped and kth person is killed in circle. The task is to choose the place in the initial circle so that you are the last one remaining and so survive. For example, if n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1…arrow_forwardThe maze is described as a graph with a start, goal, edge lengths, and two types of edges: regular paths in the maze, and hedges which one can crawl through. We are only allowed to crawl through edge once. (Some parts of the maze are too thick to crawl through.) Design an algorithm which finds the shortest path to the goal, as quickly as possible. Please do not use the modified version of Dijkstra. Instead modify the graph and use regular version of Dijkstraarrow_forward1. Write a program (WAP) to create an undirected graph using adjacency matrix representation.Number of nodes and edges should be taken from the user. After creating the graph, performfollowing operations: (i) Search a node. Take the node number from the user. If the node is found then print its associatededges.(ii) Insert a node in the graph.(iii) Insert an edge in the graph. Take the node numbers from the user between which the edge is tobe inserted.(iv) Delete a node from the graph. Take the node number to be deleted from the user.(v) Apply DFS on the graph and print the graph traversal.(vi) Apply BFS on the graph and print the graph traversal.2. Solve the above problem using adjacency list representation.arrow_forward
- Implement a program that performs a depth-first search on the graph shown in Figure.arrow_forwardin C language implement a graph coloring method that assigns the minimum color to each vertex so it does conflict with vertices that have been colored (using adjacency list)arrow_forwardIn hill-climbing algorithms there are steps that make lots of progress and steps that make very little progress. For example, the first iteration on the input given might find a path through the augmentation graph through which a flow of 30 can be added. It might, however, find the path through which only a flow of 2 can be added. How bad might the running time be when the computation is unlucky enough to always take the worst legal step allowed by the algorithm? Start by taking the step that increases the flow by 2 for the input. Then continue to take the worst possible step. You could draw out each and every step, but it is better to use this opportunity to use loop invariants. What does the flow look like after i iterations? Repeat this process on the same graph except that the four edges forming the square now have capacities 1,000,000,000,000,000 and the crossover edge has capacity 1. (Also move t to c or give that last edge a large capacity.)1. What is the worst case number of…arrow_forward
- Implement PageRank algorithm in python using following graph. Given the below graph data, implement a python program for the following steps. Import this graph to Python and visualize the graph and Using the PageRank Algorithm find top-4 important users that Canadian Tire can target for advertising.arrow_forwardThe 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_forwardUndirected graph is given with the list of edges. Build an adjacency matrix. Print the number of ones in adjacency matrix. Graph can contain multiple edges and loops. Input First line contains number of vertices n. Each of the next line contains one edge. Read the edges till the end of file. Output Build an adjacency matrix. Print the number of ones in adjacency matrix. Sample input 3 1 2 23 22 32 Sample output 5arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Database System ConceptsComputer ScienceISBN:9780078022159Author:Abraham Silberschatz Professor, Henry F. Korth, S. SudarshanPublisher:McGraw-Hill EducationStarting Out with Python (4th Edition)Computer ScienceISBN:9780134444321Author:Tony GaddisPublisher:PEARSONDigital Fundamentals (11th Edition)Computer ScienceISBN:9780132737968Author:Thomas L. FloydPublisher:PEARSON
- C How to Program (8th Edition)Computer ScienceISBN:9780133976892Author:Paul J. Deitel, Harvey DeitelPublisher:PEARSONDatabase Systems: Design, Implementation, & Manag...Computer ScienceISBN:9781337627900Author:Carlos Coronel, Steven MorrisPublisher:Cengage LearningProgrammable Logic ControllersComputer ScienceISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
Database System Concepts
Computer Science
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:9780134444321
Author:Tony Gaddis
Publisher:PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:9780132737968
Author:Thomas L. Floyd
Publisher:PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:9780133976892
Author:Paul J. Deitel, Harvey Deitel
Publisher:PEARSON
Database Systems: Design, Implementation, & Manag...
Computer Science
ISBN:9781337627900
Author:Carlos Coronel, Steven Morris
Publisher:Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:9780073373843
Author:Frank D. Petruzella
Publisher:McGraw-Hill Education