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Consider the following directed graph, which is given in adjacency list form and where vertexes have...
1. Consider the directed graph on the right side of the following page and complete the exercises below. When conducting a search, be very careful (since a small error early on can result in a large deduction of marks), and whenever you have a "choice" of which adjacent vertex to consider, you must consider the vertices in numerical order from least to greatest. (10 marks total) a. Provide an adjacency list representation of this graph. b. Compute the depth-first search...
Consider the adjacency list represention of an undirected graph 0: 6, 4, 2, 9 1: 3 2: 0 3: 7, 6, 1 4: 6, 5, 7, 0 5: 4 6: 7, 4, 3, 0 7: 8, 6, 4, 3 8: 9, 7 9: 8, 0 give the preorder traversal when running depth first search from vertex 0 using the adjacency list represented above
3. Given a directed graph G < V E >, we define its transpose Gr < V.E1 > to be the graph such that ET-{ < v, u >:< u, v >EE). In other words, GT has the same number of edges as in G, but the directions of the edges are reversed. Draw the transpose of the following graph: ta Perform DFS on the original graph G, and write down the start and finish times for each vertex in...
Consider the following directed graph for each of the problems: 1. Perform a breadth-first search on the graph assuming that the vertices and adjacency lists are listed in alphabetical order. Show the breadth-first search tree that is generated. 2. Perform a depth-first search on the graph assuming that the vertices and adjacency lists are listed in alphabetical order. Classify each edge as tree, back or cross edge. Label each vertex with its start and finish time. 3. Remove all the...
3. (8 points-7+1) Figure 4 shows an undirected graph G. Assume that the adjacency list lists the edges in alphabetical order. Figure 3: Graph for P3 (a) Apply depth first search (DFS) to graph G, and show the discovery and finish times of each vertex. In the main-loop of DFS, check the vertices in alphabetical the form dsc/fin, where dsc is the discovery time and fin is the finish time. (b) Draw the DFS tree obtained. 3. (8 points-7+1) Figure...
The following is an adjacency matrix of a directed graph. Start from vertex D, write down the order of node visited in Breadth-First- Search (BFS) traversal. (Enter the nodes in order in the following format: [A B C D E F G]) Adjacenc y Matrix ABCDEFG A 1111 000 BO00 0101 C0111010 DO 0 1 0 0 1 1 E 0 1 0 1 000 F 100 1 100 G0000100
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?
Exercise (15 points) Consider an adjacency-list representation of a directed graph G=(V.E). a) Propose in pseudocode an algorithm A to compute the in-degree of each vertex in V. b) What is the time complexity of A? c) Propose in pseudocode an algorithm B to compute the out-degree of each vertex in V. d) What is the time complexity of B?
from collections import defaultdict # This class represents a directed graph using # adjacency list representation class Graph: # Constructor def __init__(self): # default dictionary to store graph self.graph = defaultdict(list) # function to add an edge to graph def addEdge(self,u,v): self.graph[u].append(v) # Function to print a BFS of graph def BFS(self, s): # Mark all the vertices as not visited visited = [False] * (len(self.graph)) # Create a queue for BFS queue...
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