(a) Draw all binary trees with n nodes that satisfy the balance requirement of AVL trees. Assume m= 1, 2, 3, 4, 5. (b) Draw a binary tree of height 4 which will also be an AVL tree (here, define height of leaf node = 0, and height of root node = 4), and which has the smallest number of nodes among all such trees

(a) Draw all binary trees with n nodes that satisfy the balance requirement of AVL trees. Assume m= 1, 2, 3, 4, 5. (b) Draw a binary tree of height 4 which will also be an AVL tree (here, define height of leaf node = 0, and height of root node = 4), and which has the smallest number of nodes among all such trees

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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(a) Draw all binary trees with n nodes that satisfy the balance requirement of AVL trees. Assume
n = 1, 2, 3, 4, 5.
node
(b) Draw a binary tree of height 4 which will also be an AVL tree (here, define height of leaf
= 0, and height of root node = 4), and which has the smallest number of nodes among all such
trees.

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(b) (i) Define the structure of a binary tree. Explain the algorithm for inserting a number onto a binary tree such that the numbers on the tree can be traversed in a sorted manner. You do not need to explain the process of traversal. Draw the binary tree created by the algorithm when it inserts these numbers one by one from left to right: (ii) 9, –16, 8, 12, 32, 21, 4, -6, 8, 14,–2, –20, 40
[Note: Assume height of leaf node = 0 and height of root node = h. For (a) and (b), you need to explain the number of nodes at each level of the binary tree. For answering part (c), use the results in (a) and (b)]
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