Please all solve the question Question 1Which of the following graph representations would be the most performant for a graph where:• Each vertex has at most three edges incident on itThe predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations areused equally oftenAssume that the computers being used do not have memory constraints.(a) OAdjacency Matrix(b) OAdjacency List(c) OArray of EdgesQuestion 2Consider the components algorithm from the lectures that assigns vertices to connected components. What is the worst case timecomplexity of the algorithm, assuming that the graph uses the adjacency matrix representation?Note: In the time complexities below, V and E refer to the number of vertices and edges in the graph respectively.(a) O(b) OO(V^2)(c) OO(V^3)(d) OO(V + E)(e) OOVV + E))

Defined the given graph statements of correct graph representation

Question 1 Which of the following graph representations would be the most performant for a graph where: • Each vertex has at most three edges incident on it The predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations are used equally often Assume that the computers being used do not have memory constraints. (a) O Adjacency Matrix Adiacency List

Question 1 Which of the following graph representations would be the most performant for a graph where: • Each vertex has at most three edges incident on it The predominant operations used are: (1) inserting an edge, (2) removing an edge and (3) traversal, and these operations are used equally often Assume that the computers being used do not have memory constraints. (a) O Adjacency Matrix Adiacency List

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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5. A social graph is the representation, through a graph, of the virtual relationships that a user has within a social network. For example, in a social graph, vertices can represent users and edges can represent relationships between users. Under this concept, give a recursive definition of all users that are related to a user u in a social network.
1. 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.
Question 6 A graph can be presented pictorially. The vertices are drawn as circles and a label inside the circle represents the vertex. Each vertex connected with each other through a line. Each line may be directed or undirected. (a) List TWO (2) applications that may implement graph data structure concept. (b) Consider the graph shows in Figure 3 and answer the following questions: Figure 3: Directed graph i. Write down the order in which the vertices will be visited by a depth first search starting from the node A. If there are multiple valid choices, then assume that the alphabetically earlier vertices will be visited first. Show your working steps.
1. 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
Assignment on Graph A social graph contains all the friendship relations (edges) among a group of n people (vertices). The friendship relationship is symmetric. Two vertices with no edge between them are enemies. Design and implement a class called Graph for a social graph. It should have an adjacency matrix as a data member to represent the graph. The nodes in the graph are numbered from 0..n-1 graph[i][i] - is always true (1) graph[i][j] is true if i and j are friends and false (0) if they are enemies. • In the constructor, initialize all entries to false (0) and all graph[i][i] to true (1) Include the following member functions. o void makeFriends(int i,intj)- make i and j friends int countFriends(int i) - will return the number of friends of i, excluding itself int countEnemies(int i)- will return the number of enemies of i int countCommonFriends(int i,intj) - the number of common friends of i and j int countCommonEnemies(int i,intj) - the number of common enemies of i and j int…
II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task Ti requires task I, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I₁, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T₁. Task I, is an indirect dependency of task I, if there is no edge from T, to T, but I must appear before 7, in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁,…
DATA STRUCTURES AND ALGORITHMS C++ Draw a directed graph from the following adjacency list. Simulate/dry run your algorithm on it and provide step-by-step updates of values in used data structure(s) considering “A” as source and “J” asdestination.
Question-Path Search in A MazeA two dimensional array of red and green entries represents a maze. Green entries are passable and red entries are blocked (like a wall). Two special green entries en and ex denote the entrance and exit of the maze.(1) Abstract the problem as a graph;(2) Design an algorithm (pseudo code) to find a path from en to ex if it exists and then print out the path;(3) Analyze the complexity of the algorithm.
II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task Ti requires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T₁ and T₁, determines if task T₁ can be performed without performing task Tj. Note that T; is not required if it is not a direct or indirect dependency of Ti. Task T; is an indirect dependency of task T; if there is no edge from T; to T; but I must appear before T; in the topological order. b. Describe an algorithm that runs in O(n + m) time that given a task T₁,…
II. Read each problem carefully and present an algorithm with the required running-time to solve each problem. 1. In class we discussed that directed acyclic graphs (DAG) can be used to represent dependency/precedence relations. One example is modeling task dependency where tasks are represented as vertices and edges represents direct dependencies between tasks, e.g., if task Ti requires task T, then there is an edge from vertex i to vertex j. Arranging tasks with respect to their dependencies can easily be done by performing topological sort to the DAG. a. Describe an algorithm that runs in O(n + m) time that given two tasks, T, and I, determines if task T, can be performed without performing task T₁. Note that I, is not required if it is not a direct or indirect dependency of T₁. Task I, is an indirect dependency of task I, if there is no edge from T, to T, but T, must appear before 7, in the topological order.
data structure and algorithm 1. Build an adjacency matrix for the graph in the figure below 2. Build a list of successors for the graph in the figure below 3. Given an adjacency matrix representing a graph, write a function to find all vertices with O out-degree m n u
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.