b) One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1. Starting with an empty BST and AVL tree, insert the following keys into the two trees (BST as well as AVL trees): 17, 28, 10, 25, 27, 12, 32, 28. If a key is already existed, insert the new key to the right sub-tree.

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
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b) One main difference between a binary search tree (BST) and an AVL (Adelson-Velski
and Landis) tree is that an AVL tree has a balance condition, that is, for every node
in the AVL tree, the height of the left and right subtrees differ by at most 1. Starting
with an empty BST and AVL tree, insert the following keys into the two trees (BST
as well as AVL trees):
17, 28, 10, 25, 27, 12, 32, 28
If a key is already existed, insert the new key to the right sub-tree.
c) Based on what you have done for Question 3b, what is the big-O (worst case)
complexity of the total time required to build a binary search tree (BST) consisting
of n nodes? Explain your answer. Answer without explanation gains no mark. (Hint.
A tricky question. The question asks for worst case complexity. Think properly.)
d) Similarly, from what you have done for Question 3c, what is the big-o (worst case)
complexity of the total time required to build an AVL tree consisting of n nodes?
Explain your answer. Answer without explanation gains no mark. (Hint. The question
asks for worst case complexity.)
Transcribed Image Text:b) One main difference between a binary search tree (BST) and an AVL (Adelson-Velski and Landis) tree is that an AVL tree has a balance condition, that is, for every node in the AVL tree, the height of the left and right subtrees differ by at most 1. Starting with an empty BST and AVL tree, insert the following keys into the two trees (BST as well as AVL trees): 17, 28, 10, 25, 27, 12, 32, 28 If a key is already existed, insert the new key to the right sub-tree. c) Based on what you have done for Question 3b, what is the big-O (worst case) complexity of the total time required to build a binary search tree (BST) consisting of n nodes? Explain your answer. Answer without explanation gains no mark. (Hint. A tricky question. The question asks for worst case complexity. Think properly.) d) Similarly, from what you have done for Question 3c, what is the big-o (worst case) complexity of the total time required to build an AVL tree consisting of n nodes? Explain your answer. Answer without explanation gains no mark. (Hint. The question asks for worst case complexity.)
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