Remember, in our definition, the height of a binary tree means maximum number of nodes from the root to a leaf. a) In a perfect binary tree of size n, what is the tree's exact height? Justify your answer. b) In a degenerate binary tree of size n, what is the tree's exact height? Justify your answer. c) What is the maximum height for a balanced binary tree of size 7? Justify your answer
Remember, in our definition, the height of a binary tree means maximum number of nodes from the root to a leaf. a) In a perfect binary tree of size n, what is the tree's exact height? Justify your answer. b) In a degenerate binary tree of size n, what is the tree's exact height? Justify your answer. c) What is the maximum height for a balanced binary tree of size 7? Justify your answer
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Question
Remember, in our definition, the height of a binary tree means maximum number of nodes from the root to a leaf.
a) In a perfect binary tree of size n, what is the tree's exact height? Justify your answer.
b) In a degenerate binary tree of size n, what is the tree's exact height? Justify your answer.
c) What is the maximum height for a balanced binary tree of size 7? Justify your answer
Expert Solution
Step 1
Here is your solution:
a). Perfect binary tree:
A binary tree in which every node has exactly two child nodes and all the leaf node are at the same level.
A perfect binary tree of height h, has (2h+1 - 1) node
So, A perfect binary tree with n nodes has height, log(n+1) -1
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