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Consider the Fibonacci sequence F(0)=0, F(1)=1 and F(i)=F(i-1}+F(i-2) for i > 1. For the sake of this exercise we define the height of a tree as the maximum number of vertices of a root-to-leaf path. In particular, the height of the empty tree is zero, and the height of a tree with a single vertex is one. Prove that the number of nodes of an AVL tree of height h is at least F(h) and this inequality is tight only for two values of h.

Consider the Fibonacci sequence F(0)=0, F(1)=1 and F(i)=F(i-1}+F(i-2) for i > 1. For the sake of this exercise we define the height of a tree as the maximum number of vertices of a root-to-leaf path. In particular, the height of the empty tree is zero, and the height of a tree with a single vertex is one. Prove that the number of nodes of an AVL tree of height h is at least F(h) and this inequality is tight only for two values of h.

Computer Networking: A Top-Down Approach (7th Edition)
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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Consider the Fibonacci sequence F(0)=0, F(1)=1 and F(i)=F(i-1)+F(i-2) for i>1. For the sake of this exercise we define the height of a tree as the maximum number of vertices of a root-to-leaf path. In particular, the height of the empty tree is zero, and the height of a tree with a single vertex is one. Prove that the number of nodes of an AVL tree of height h is at least F(h) and this inequality is tight only for two values of h.
Transcribed Image Text:Consider the Fibonacci sequence F(0)=0, F(1)=1 and F(i)=F(i-1)+F(i-2) for i>1. For the sake of this exercise we define the height of a tree as the maximum number of vertices of a root-to-leaf path. In particular, the height of the empty tree is zero, and the height of a tree with a single vertex is one. Prove that the number of nodes of an AVL tree of height h is at least F(h) and this inequality is tight only for two values of h.
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