Determine a formula that expresses the height of the tree. Answer: General Recursion Tree: 1 1 = 2° 2 = 2! T(n/2) T(n/2) 4 = 22 T(n/4) T(n/4) T(n/4) T(n/4) og n T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) 8 = 23 T(1) T(1) T(1) T(1) T(1) T(1) n = 2k ....
Determine a formula that expresses the height of the tree. Answer: General Recursion Tree: 1 1 = 2° 2 = 2! T(n/2) T(n/2) 4 = 22 T(n/4) T(n/4) T(n/4) T(n/4) og n T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) T(n/8) 8 = 23 T(1) T(1) T(1) T(1) T(1) T(1) n = 2k ....
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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Transcribed Image Text:• Determine a formula that expresses the height of the tree.
Answer: General Recursion Tree:
1
1 = 2°
2 = 2!
T(n/2)
T(n/2)
4 = 22
T(n/4)
T(n/4)
T(n/4)
T(n/4)
log n
T(n/8)
T(n/8)
T(n/8)
T(n/8)
T(n/8)
T(n/8)
T(n/8)
T(n/8)
8 = 23
T(1)
T(1)
T(1)
T(1)
T(1)
T(1)
n= 2k
........
Therefore the height of the binary tree is log2 n
And because we have a binary tree the formula to find the number of nodes would
be 2-1 – 1 = 2logn+1 - 1
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