Consider the following algorithm for generating a tree on N vertices: Number the vertices 1 to N. Processing the vertices in order, draw an edge between vertex i and one of the previous vertices {1, 2, 3, ..., i-1}, selected uniformly at random. Part A: Write a program to generate trees in this way. Draw an example tree this produces on 20 vertices. Do you think this program can generate every possible tree of a given size? Why or why
Consider the following algorithm for generating a tree on N vertices: Number the vertices 1 to N. Processing the vertices in order, draw an edge between vertex i and one of the previous vertices {1, 2, 3, ..., i-1}, selected uniformly at random. Part A: Write a program to generate trees in this way. Draw an example tree this produces on 20 vertices. Do you think this program can generate every possible tree of a given size? Why or why
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Answer the following parts accordingly. Thanks in advance!
![Consider the following algorithm for generating a tree on N vertices:
Number the vertices 1 to N.
Processing the vertices in order, draw an edge between vertex i and one of the previous
vertices {1, 2, 3, ..., i-1}, selected uniformly at random.
Part A: Write a program to generate trees in this way. Draw an example tree this produces on 20
vertices. Do you think this program can generate every possible tree of a given size? Why or why
not? Do you think this program generates trees uniformly at random from the set of trees? Why
or why not?
Part B: Use your program to generate a graph of 'umber of vertices N' vs 'avg # of leaves' using
this algorithm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2fbff82e-583d-4003-b329-07736a7bbd92%2Fbdc026a2-a9d1-4ffc-bfff-e4f30027be90%2Fzpx3t2m_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following algorithm for generating a tree on N vertices:
Number the vertices 1 to N.
Processing the vertices in order, draw an edge between vertex i and one of the previous
vertices {1, 2, 3, ..., i-1}, selected uniformly at random.
Part A: Write a program to generate trees in this way. Draw an example tree this produces on 20
vertices. Do you think this program can generate every possible tree of a given size? Why or why
not? Do you think this program generates trees uniformly at random from the set of trees? Why
or why not?
Part B: Use your program to generate a graph of 'umber of vertices N' vs 'avg # of leaves' using
this algorithm.
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