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What is the height of the perfect binary tree shown below?

What is the height of the perfect binary tree shown below?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Fill in the Blank** **Exercise 7.8.8: The height of a perfect binary tree.** The function \( h \) maps every perfect binary tree to a non-negative integer. \( h(T) \) is called the height of tree \( T \). The function \( h \) is defined recursively as follows: - If \( T \) is the perfect binary tree that consists of a single vertex, then \( h(T) = 0 \). - Suppose that the tree \( T' \) is constructed by taking two copies of perfect binary tree \( T \), adding a new vertex \( v \) and adding edges between \( v \) and the roots of each copy of \( T \). Then \( h(T') = h(T) + 1 \). **What is the height of the perfect binary tree shown below?** **Diagram Description:** The diagram shows a perfect binary tree with three vertices. At the top, there is one vertex (root), and it connects to two vertices at the next level. This tree is symmetrical, typical of a perfect binary tree where each node has exactly two children. The height of this tree is 1, as the height is the number of edges on the longest path from the root to a leaf.
Transcribed Image Text:**Fill in the Blank** **Exercise 7.8.8: The height of a perfect binary tree.** The function \( h \) maps every perfect binary tree to a non-negative integer. \( h(T) \) is called the height of tree \( T \). The function \( h \) is defined recursively as follows: - If \( T \) is the perfect binary tree that consists of a single vertex, then \( h(T) = 0 \). - Suppose that the tree \( T' \) is constructed by taking two copies of perfect binary tree \( T \), adding a new vertex \( v \) and adding edges between \( v \) and the roots of each copy of \( T \). Then \( h(T') = h(T) + 1 \). **What is the height of the perfect binary tree shown below?** **Diagram Description:** The diagram shows a perfect binary tree with three vertices. At the top, there is one vertex (root), and it connects to two vertices at the next level. This tree is symmetrical, typical of a perfect binary tree where each node has exactly two children. The height of this tree is 1, as the height is the number of edges on the longest path from the root to a leaf.
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