Answered: Suppose we have an array A of n…

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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Suppose we have an array A of n distinct elements. We will show that any BST T containing all elements in A can be converted into any other BST R containing all elements in A using O(n) rotations. (Recall that there may be many valid BST configurations (shapes) for a given data set.) (a) In a few sentences, explain how you can apply O(n) right rotations on T such that the resulting tree is only a single path (i.e., a straight line from the root to the rightmost possible leaf; this is called the right spine). In a right spine, every node except the root and some of the leaves is a right child. (b) Say we want to transform the new tree back into T. What would we do? (c) Using your answers to the above questions, design an algorithm to trans- form any tree T into any other tree R in O(n) time.

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