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1. Consider the directed graph on the right side of the following page and complete the...
Consider the following directed graph for each of the problems: 1. Perform a breadth-first search on...
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...
Give the adjacency matrix representation and the adjacency lists representation for the graph G_1. Assume that...
Give the adjacency matrix representation and the adjacency lists representation for the graph G_1. Assume that vertices (e.g., in adjacency lists) are ordered alphabetically. For the following problems, assume that vertices are ordered alphabetically in the adjacency lists (thus you will visit adjacent vertices in alphabetical order). Execute a Breadth-First Search on the graph G_1, starting on vertex a. Specifiy the visit times for each node of the graph. Execute a Depth-First Search on the graph G_1 starting on vertex...
3. Given a directed graph G < V E >, we define its transpose Gr < V.E1 > to be the graph such tha...
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, which is given in adjacency list form and where vertexes have...
Consider the following directed graph, which is given in adjacency list form and where vertexes have numerical labels: 1: 2, 4, 6 2: 4, 5 3: 1, 2, 6, 9 4: 5 5: 4, 7 6: 1, 5, 7 7: 3, 5 8: 2, 6, 7 9: 1, 7 The first line indicates that the graph contains a directed edge from vertex 1 to vertex 2, from 1 to vertex 4, and 1 to 6, and likewise for subsequent lines....
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above...
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T. b.[3] Find a Breadth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T.
(5 marks) a. The pseudo-code for breadth-first search, modified slightly from Drozdek,1 is as follows: void...
(5 marks) a. The pseudo-code for breadth-first search, modified slightly from Drozdek,1 is as follows: void breadthFirstSearch (vertex w) for all vertices u num (u) 0 null edges i=1; num (w) i++ enqueue (w) while queue is not empty dequeue ( V= for all vertices u adjacent to v if num(u) is 0 num (u) = i++; enqueue (u) attach edge (vu) to edges; output edges; Now consider the following graph. Give the breadth-first traversal of the graph, starting from...
from collections import defaultdict # This class represents a directed graph using # adjacency list...
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...
Question II - Graph Traversal and Minimum Spanning Trees [40 Points] Consider the following graph: B...
Question II - Graph Traversal and Minimum Spanning Trees [40 Points] Consider the following graph: B 10 1 4 1 H 9 4 a) Traverse the graph starting from vertex A, and using the Breadth-First Search algorithm. Show the traversal result and the data structure you are using. [10 Points] b) Traverse the graph starting from vertex A, and using the Depth-First Search (Post-order) algorithm. Show the traversal result and the data structure you are using. [10 Points] c) Apply...
help with alogrthms Consider the following graph for problems 6, 7, & 8. (b f C...
help with alogrthms
Consider the following graph for problems 6, 7, & 8. (b f C d a (5 points) Starting at vertex a and resolving ties by the vertex alphabetical order, traverse the graph by depth-first search 7. and construct the corresponding depth-first search tree (5 points) Traverse the graph by breadth-first search and construct the corresponding breadth-first search tree. Start the 8. traversal at vertex a and resolve ties by the vertex alphabetical order.
Consider the following graph...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
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...
Give the adjacency matrix representation and the adjacency lists representation for the graph G_1. Assume that vertices (e.g., in adjacency lists) are ordered alphabetically. For the following problems, assume that vertices are ordered alphabetically in the adjacency lists (thus you will visit adjacent vertices in alphabetical order). Execute a Breadth-First Search on the graph G_1, starting on vertex a. Specifiy the visit times for each node of the graph. Execute a Depth-First Search on the graph G_1 starting on vertex...
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, which is given in adjacency list form and where vertexes have numerical labels: 1: 2, 4, 6 2: 4, 5 3: 1, 2, 6, 9 4: 5 5: 4, 7 6: 1, 5, 7 7: 3, 5 8: 2, 6, 7 9: 1, 7 The first line indicates that the graph contains a directed edge from vertex 1 to vertex 2, from 1 to vertex 4, and 1 to 6, and likewise for subsequent lines....
7.[6] Consider the graph G below: a.[3] Find a Depth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T. b.[3] Find a Breadth-First Search tree T for the above graph starting with the vertex 0. Show all the vertices as they are discovered in sequence starting from 1 to the last vertex included in T.
(5 marks) a. The pseudo-code for breadth-first search, modified slightly from Drozdek,1 is as follows: void breadthFirstSearch (vertex w) for all vertices u num (u) 0 null edges i=1; num (w) i++ enqueue (w) while queue is not empty dequeue ( V= for all vertices u adjacent to v if num(u) is 0 num (u) = i++; enqueue (u) attach edge (vu) to edges; output edges; Now consider the following graph. Give the breadth-first traversal of the graph, starting from...
Question II - Graph Traversal and Minimum Spanning Trees [40 Points] Consider the following graph: B 10 1 4 1 H 9 4 a) Traverse the graph starting from vertex A, and using the Breadth-First Search algorithm. Show the traversal result and the data structure you are using. [10 Points] b) Traverse the graph starting from vertex A, and using the Depth-First Search (Post-order) algorithm. Show the traversal result and the data structure you are using. [10 Points] c) Apply...
help with alogrthms
Consider the following graph for problems 6, 7, & 8. (b f C d a (5 points) Starting at vertex a and resolving ties by the vertex alphabetical order, traverse the graph by depth-first search 7. and construct the corresponding depth-first search tree (5 points) Traverse the graph by breadth-first search and construct the corresponding breadth-first search tree. Start the 8. traversal at vertex a and resolve ties by the vertex alphabetical order.
Consider the following graph...
2. This question concerns the graph G shown below. (a) Mark the spanning tree for G obtained by performing a depth-first search starting at the vertex A, and using the convention that nearby vertices should be explored in a counter-clockwise fasion, beginning with east; so E comes first, then NE, then N, ... (b) Mark the spanning tree for G obtained by performing a breadth-first search starting at the vertex A, and using the convention that nearby vertices should be...
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