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For any binary tree T, let I(T) be the number of internal nodes and let L(T) be the number of leaf nodes. Use the Second Principle of Mathematical Induction to prove the following: For any integer h > 0, any full binary tree T of height h satisfies the following equation: I(T) = L(T) – 1 [Important note: You can think of any binary tree as consisting of: the root node, possibly a left subtree (which is itself a binary tree) and possibly a right subtree (which is itself a binary tree). This should be helpful to you during the inductive step.]

For any binary tree T, let I(T) be the number of internal nodes and let L(T) be the number of leaf nodes. Use the Second Principle of Mathematical Induction to prove the following: For any integer h > 0, any full binary tree T of height h satisfies the following equation: I(T) = L(T) – 1 [Important note: You can think of any binary tree as consisting of: the root node, possibly a left subtree (which is itself a binary tree) and possibly a right subtree (which is itself a binary tree). This should be helpful to you during the inductive step.]

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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A binary tree is sometimes called full if every node has either 0 or 2
children (i.e., if there are no nodes that have only one child).

For any binary tree T, let I(T) be the number of internal nodes and let L(T) be the number of leaf nodes. Use the Second Principle of Mathematical Induction to prove the following: For any integer h > 0, any full binary tree T of height h satisfies the following equation: I(T) = L(T) – 1 [Important note: You can think of any binary tree as consisting of: the root node, possibly a left subtree (which is itself a binary tree) and possibly a right subtree (which is itself a binary tree). This should be helpful to you during the inductive step.]
Transcribed Image Text:For any binary tree T, let I(T) be the number of internal nodes and let L(T) be the number of leaf nodes. Use the Second Principle of Mathematical Induction to prove the following: For any integer h > 0, any full binary tree T of height h satisfies the following equation: I(T) = L(T) – 1 [Important note: You can think of any binary tree as consisting of: the root node, possibly a left subtree (which is itself a binary tree) and possibly a right subtree (which is itself a binary tree). This should be helpful to you during the inductive step.]
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