binomial tree, Bn is defined recursively as follows. B0 is the tree with a single vertex. Create Bn+1, where n is a nonegative integer, by making two copies of Bn; the first copy becomes the root tree of Bn+1, and the second copy becomes the leftmost child of the root in the first copy. Here are examples for n = 0 to 3: Draw the binomial tree for n = 4 (it pays to do this neatly and carefully as it will makes the rest of the questions easier to answer). Create a table that has the depth of each of B0 to B4 (note that B0 has a depth of 1). Determine the formula for these as a function of n, and include in your table your calculation for B5 (you should NOT have to draw B5!). Create a table that has the number of nodes in each of B0 to B4. Determine the formula for these as a function of n, and include in your table your calculation for B5 (you should NOT have to draw B5!).

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
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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    1. binomial tree, Bn is defined recursively as follows.

B0 is the tree with a single vertex.
Create Bn+1, where n is a nonegative integer, by making two copies of Bn; the first copy becomes the root tree of Bn+1, and the second copy becomes the leftmost child of the root in the first copy.
Here are examples for n = 0 to 3:

  1. Draw the binomial tree for n = 4 (it pays to do this neatly and carefully as it will makes the rest of the questions easier to answer).
  2. Create a table that has the depth of each of B0 to B4 (note that B0 has a depth of 1). Determine the formula for these as a function of n, and include in your table your calculation for B5 (you should NOT have to draw B5!).
  3. Create a table that has the number of nodes in each of B0 to B4. Determine the formula for these as a function of n, and include in your table your calculation for B5 (you should NOT have to draw B5!).
3.
B,
Transcribed Image Text:3. B,
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