To augment a red-black tree, consider storing the following information at each node x of the tree. (You may store additional information as well.) Keys are integers. For each of (a)-(e), answer whether or not it's a good idea to do it, for an efficient augmented red-black tree. Each question is independent. (a) the number of nodes in the left subtree of x good idea O bad idea (b) the product of the number of nodes in the left subtree of x and the number of nodes in the right subtree of x O good idea O bad idea (c) distance from x to the root of the tree O good idea bad idea (d) the number of nodes with key equal to 7 (a fixed constant) in the subtree of x O good idea O bad idea

To augment a red-black tree, consider storing the following information at each node x of the tree. (You may store additional information as well.) Keys are integers. For each of (a)-(e), answer whether or not it's a good idea to do it, for an efficient augmented red-black tree. Each question is independent. (a) the number of nodes in the left subtree of x good idea O bad idea (b) the product of the number of nodes in the left subtree of x and the number of nodes in the right subtree of x O good idea O bad idea (c) distance from x to the root of the tree O good idea bad idea (d) the number of nodes with key equal to 7 (a fixed constant) in the subtree of x O good idea O bad idea

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

(e) the number of nodes in the entire tree with even keys larger than the key of
O good idea
bad idea
(f) Pick one from (a)-(e) for which your answer is GOOD idea and explain why:
GOOD idea choice:
Enter your answer here
Explanation:
Enter your answer here
(c) Pick one from (a)-(e) for which your answer is BAD idea and explain why:
BAD idea choice:
Enter your answer here
Explanation:
Enter your answer

To augment a red-black tree, consider storing the following information at each node x of the
tree. (You may store additional information as well.) Keys are integers.
For each of (a)-(e), answer whether or not it's a good idea to do it, for an efficient augmented
red-black tree. Each question is independent.
(a) the number of nodes in the left subtree of x
O good idea
O bad idea
(b) the product of the number of nodes in the left subtree of x and the number of nodes in the
right subtree of x
O good idea
O bad idea
(c) distance from x to the root of the tree
O good idea
bad idea
(d) the number of nodes with key equal to 7 (a fixed constant) in the subtree of x
O good idea
O bad idea

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Q1. Consider the following sequence of numbers: 15, 20, 24, 10, 13, 7, 30, 36, and 25. Insert these numbers one by one into an initially empty red-black tree, and illustrate the tree after each insertion. rotation is needed, present the status before and after the rotation and indicate which rotation is applied. For each node, indicate the color for each node like 15(RED) or 30(BLACK), Ensure that the tree maintains its red-black properties throughout the process. Q2. Given the following sets: A = {2, 4, 6, 8, 10}, B = {1, 3, 5, 7, 9}, C = {1, 2, 3, 4, 5}, and D = {5, 6, 7, 8, 9). Calculate the following set operations and provide the resulting sets: A U B, An C, B n D, (A U B) - C, and (C n D) A (AN B).
Problem 3 Recall from lecture that a binary tree T is either: 1. null (the empty tree); or 2. a root noder with two subtrees T₁ and TR, both of which are binary trees. Consider the following algorithm numLeaves (T) that takes as input a binary tree T and returns the number of leaves in the tree. numLeaves (T): 1: if T == null then return 0 2: 3: else 4: 5: 6: 7: 8: TL, TR the left and right subtrees of T, respectively if T₁ == null and TR == null then return 1 else return numLeaves (TL) + numLeaves (TR) Prove by structural induction that for every binary tree T, numLeaves (T) returns the number of leaves of T.