12. (A)Is the following tree a valid AVL tree? Why or why not?(B)Is the following tree a valid AVL tree? Why or why not?(C)What is the minimum number of nodes in an AVL tree of height 15?

For a tree to be a valid AVL tree balancing factors of each of its nodes need to be either -1,0 or…

Answered: 12. (A) Is the following tree a valid…

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

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12. (A)
Is the following tree a valid AVL tree? Why or why not?
(B)
Is the following tree a valid AVL tree? Why or why not?
(C)
What is the minimum number of nodes in an AVL tree of height 15?

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Step 1

For a tree to be a valid AVL tree balancing factors of each of its nodes need to be either -1,0 or 1.
Balancing factor = Height of the left subtree - the height of the right subtree.
Minimum no. of nodes in an AVL tree of height h is defined by a recursive relation :

f(h) = f(h-1) + f(h-2) + 1, and f(1) = 0 , f(2) = 1 where h represents the height of AVL Tree.

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