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Exercise (15 points) Consider an adjacency-list representation of a directed graph G=(V.E). a) Propose in pseudocode...
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...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the number of edges (a) Design an algorithm (give pseudocode) that, given a vertex v EV, computes the in-degree of v under (b) Design an algorithm (give pseudocode) that, given a vertex v E V, computes the in-degree of v incident into v. the assumption that G is represented by an adjacency list. Give an analysis of your algorithm. under the assumption that G is...
22.1-1 Given an adjacency-list representation of a directed graph, how long does it take to compute...
22.1-1 Given an adjacency-list representation of a directed graph, how long does it take to compute the out-degree of every vertex? How long does it take to compute the in-degrees?
Assume that the adjacency list representing a directed graph G has already been constructed. Show how...
Assume that the adjacency list representing a directed graph G has already been constructed. Show how to determine whether G contains a universal sink, that is a vertex with in-degree |V | − 1 and out-degree 0, in time O(|V |). **Please explain in detail
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the gr...
This question needs to be done using pseudocode (not any
particular programming language). Thanks
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the gr...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an algorithm that returns a list containing the neighbourhood degree for each node v V,...
5. The in-degree of a vertex in a directed graph is the number of edges directed...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
Problem 3 (15 points). Let G (V,E) be the following directed graph. a. 1. Draw the...
Problem 3 (15 points). Let G (V,E) be the following directed graph. a. 1. Draw the reverse graph G of G. 2. Run DFS on G to obtain a post number for each vertex. Assume that in the adjacency list representation of G, vertices are stored alphabetically, and in the list for each vertex, its adjacent vertices are also sorted alphabetically. In other words, the DFS algorithm needs to examine all vertices alphabetically, and when it traverses the adjacent vertices...
Write the pseudocode of the Depth First Search Algorithm DFS(G) using adjacencymatrix representation of the graph...
Write the pseudocode of the Depth First Search Algorithm DFS(G)
using adjacencymatrix
representation of the graph G. What is the running time of your
pseudocode?
Specification: start from the psedocode discussed in class and
do only the modifications
needed for adjacency-matrix graph representation.
Below is the pseudocode discussed in class:
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time whe...
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time where n is the number of vertices in V.
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can...
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...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the number of edges (a) Design an algorithm (give pseudocode) that, given a vertex v EV, computes the in-degree of v under (b) Design an algorithm (give pseudocode) that, given a vertex v E V, computes the in-degree of v incident into v. the assumption that G is represented by an adjacency list. Give an analysis of your algorithm. under the assumption that G is...
22.1-1 Given an adjacency-list representation of a directed graph, how long does it take to compute the out-degree of every vertex? How long does it take to compute the in-degrees?
This question needs to be done using pseudocode (not any
particular programming language). Thanks
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an...
Consider an unweighted, undirected graph G = 〈V, E). The neighbourhood of a node u E V in the graph is the set of all nodes that are adjacent (or directly connected) to v. Subsequently, we can define the neighbourhood degree of the node v as the sum of the degrees of all its neighbours (those nodes that are directly connects to v) (a) Design an algorithm that returns a list containing the neighbourhood degree for each node v V,...
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
Problem 3 (15 points). Let G (V,E) be the following directed graph. a. 1. Draw the reverse graph G of G. 2. Run DFS on G to obtain a post number for each vertex. Assume that in the adjacency list representation of G, vertices are stored alphabetically, and in the list for each vertex, its adjacent vertices are also sorted alphabetically. In other words, the DFS algorithm needs to examine all vertices alphabetically, and when it traverses the adjacent vertices...
Write the pseudocode of the Depth First Search Algorithm DFS(G)
using adjacencymatrix
representation of the graph G. What is the running time of your
pseudocode?
Specification: start from the psedocode discussed in class and
do only the modifications
needed for adjacency-matrix graph representation.
Below is the pseudocode discussed in class:
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can be done in O(n) time where n is the number of vertices in V.
8, (10 pts) Show that given a directed graph G = (V,E) already stored in adjacency matrix form, determining if there is a vertex with in-degree n - 1 and out-degree 0 can...
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