a directed graph has n+2 vertices: 2 of these are S and T. the rest have integer labels 1...n. for every vertex labelled i, 1 is smaller than or equal to i and i is smaller than or equal to n. there i...
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a directed graph has n+2 vertices: 2 of these are S and T. the rest have integer labels 1...n. for every vertex labelled i, 1 is smaller than or equal to i and i is smaller than or equal to n. there i...
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s....
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s. Fix a destination vertex t, and assume that the graph contains at least one s-t path. Which of the following statements are true? [Check all that apply.] ( )The shortest (i.e., minimum-length) s-t path might have as many as n−1 edges, where n is the number of vertices. ( )There is a shortest s-t path with no repeated vertices (i.e., a "simple" or "loopless"...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
5. Suppose we are given an unweighted, directed graph G with n vertices (labelled 1 to...
5. Suppose we are given an unweighted, directed graph G with n vertices (labelled 1 to n), and let M be the n × n adjacency matrix for G (that is, M (i,j-1 if directed edge (1J) is in G and 0 otherwise). a. Let the product of M with itself (M2) be defined, for 1 S i,jS n, as follows where "." is the Boolean and operator and "+" is the Boolean or operator. Given this definition what does...
For a directed graph the in-degree of a vertex is the number of edges it has...
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
Question 1: Given an undirected connected graph so that every edge belongs to at least one...
Question 1: Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Question 2: Given a graph G(V, E) a set I is an independent set if for every uv el, u #v, uv & E. A Matching is a collection of edges {ei} so...
Problem 1: Dynamic Programming in DAG Let G(V,E), |V| = n, be a directed acyclic graph...
Problem 1: Dynamic Programming in DAG Let G(V,E), |V| = n, be a directed acyclic graph presented in adjacency list representation, where the vertices are labelled with numbers in the set {1, . . . , n}, and where (i, j) is and edge inplies i < j. Suppose also that each vertex has a positive value vi, 1 ≤ i ≤ n. Define the value of a path as the sum of the values of the vertices belonging to...
#include <iostream> #include <queue> using namespace std; class Graph { public: Graph(int n); ~Graph(); void addEdge(int...
#include <iostream>
#include <queue>
using namespace std;
class Graph {
public:
Graph(int n);
~Graph();
void addEdge(int src, int tar);
void BFTraversal();
void DFTraversal();
void printVertices();
void printEdges();
private:
int vertexCount;
int edgeCount;
bool** adjMat;
void BFS(int n, bool marked[]);
void DFS(int n, bool marked[]);
};
Graph::Graph(int n=0) {
vertexCount = n;
edgeCount = 0;
if(n == 0)
adjMat = 0;
else {
adjMat = new bool* [n];
for(int i=0; i < n; i++)
adjMat[i] = new bool [n];
for(int i=0;...
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the T...
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the Traveling Salesman Problem? 5. In the n-Queens problem as given in the textbook, where it is assumed that no two queens can occupy the same row on annx n chessboard, how many nodes are there in the total stat space tree without pruning? 6. As in the previous question, how many leaf nodes in the state space tree? z2 7....
Input: a directed grid graph G, a set of target points S, and an integer k...
Input: a directed grid graph G, a set of target points S, and an integer k Output: true if there is a path through G that visits all points in S using at most k left turns A grid graph is a graph where the vertices are at integer coordinates from 0,0 to n,n. (So 0,0, 0,1, 0,2, ...0,n, 1,0, etc.) Also, all edges are between vertices at distance 1. (So 00->01, 00->10, but not 00 to any other vertex....
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac,...
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
5. Suppose we are given an unweighted, directed graph G with n vertices (labelled 1 to n), and let M be the n × n adjacency matrix for G (that is, M (i,j-1 if directed edge (1J) is in G and 0 otherwise). a. Let the product of M with itself (M2) be defined, for 1 S i,jS n, as follows where "." is the Boolean and operator and "+" is the Boolean or operator. Given this definition what does...
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
#include <iostream>
#include <queue>
using namespace std;
class Graph {
public:
Graph(int n);
~Graph();
void addEdge(int src, int tar);
void BFTraversal();
void DFTraversal();
void printVertices();
void printEdges();
private:
int vertexCount;
int edgeCount;
bool** adjMat;
void BFS(int n, bool marked[]);
void DFS(int n, bool marked[]);
};
Graph::Graph(int n=0) {
vertexCount = n;
edgeCount = 0;
if(n == 0)
adjMat = 0;
else {
adjMat = new bool* [n];
for(int i=0; i < n; i++)
adjMat[i] = new bool [n];
for(int i=0;...
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the Traveling Salesman Problem? 5. In the n-Queens problem as given in the textbook, where it is assumed that no two queens can occupy the same row on annx n chessboard, how many nodes are there in the total stat space tree without pruning? 6. As in the previous question, how many leaf nodes in the state space tree? z2 7....
5. Here are the vertices and edges of directed graph G: V= {2.6.c.de.f} E= {ab, ac, af ca. bc. be.bf. cd, ce, de, df). Weights: w(ab) = 2 w(ac) = 5, w(af) = 10, w(ca) = 2. w(be) = 2. w(be) = 10, w(bf) = 11. w(cd)= 9. w(ce) = 7. w(de) = 2. w(df) = 2. a. Draw the Graph. This is a directed, weighted graph so you need to include arrows and weights. You can insert a pic...
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