Use any drawing appiication to show the steps of constructing a new red-black tree by performing a sequence of insertions for these numbers: 2, 1, 4, 5 9, 3, 6, 7. As described in the last lecture, each step of insertion or fixing up the violation should be indicated on a separate tree. So you have to start with a tree of one node (root) containing the first number (2), then the second tree involves the root

Use any drawing appiication to show the steps of constructing a new red-black tree by performing a sequence of insertions for these numbers: 2, 1, 4, 5 9, 3, 6, 7. As described in the last lecture, each step of insertion or fixing up the violation should be indicated on a separate tree. So you have to start with a tree of one node (root) containing the first number (2), then the second tree involves the root

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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Starting from an empty tree, perform the following insert operations into an AVL tree and answer the questions that follow (Q4-7). For AVL trees, make sure to check for balance after each operation and rotate if necessary before answering the question. Insert 41, 27, 10, 53, 25, 18, 32, 3, 36, 28, 30 Q4. After all operations, how many times did you have to rebalance the tree? Q5. After all operations, what is the weight of the tree? Q6. After all operations, what is the degree of node 41?
Explain how to implement a complete binary tree by using an array. Note that you have to point out how to derive the indices of a node i's parent, left child, and right child individually. Also, explain pros and cons of this representation.
Construct AVL trees by inserting the elements successively, starting with the empty tree. a) 1, 2, 3, 4, 5, 6 b) 6, 5, 4, 3, 2, 1 c) 3, 6, 5, 1, 2, 4 (Note: Observe the final trees and you will find that although all of them have the same data, the tree are not necessarily the same.)
Build an AVL tree by inserting the following sequence in order: 1 9 6 7 11 12 A NULL node can be indicated by the symbol 0 (ZERO).
Trace the construction of the AVL tree that results. Show the trees and the BFs for each node. Box in the final answer.99, 88, 77, 66, 55, 44, 33, 22, 11
[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)]
Part (a) MST: An MST T with respect to the original weights is still a MST with the new weights (of course the weight of the tree changes but the tree itself is still a MST): True or False? If you said True then give a short explanation why, and if you said False then give a counterexample (you can upload a picture). Note, you cannot assume the MST was constructed using a specific algorithm, but you can assume each edge satisfies the cut property for some cut. Part (b) Shortest paths: The shortest paths with respect to the original weights are still shortest paths with the new weights (of course the weights of the path change but the paths themselves are still shortest paths): True or False? If you said True then give a short explanation why, and if you said False then give a counterexample
A ternary tree is like a binary tree, except each node in a ternary tree may have three children: a left child, a middle child, and a right child. Write an analogue of the TreeNode declaration that can be used to represent the nodes of a ternary tree.
Problem 3. Binary Tree Q4. Given the binary tree on the picture, match the following questions with the answers. If you cannot see the picture, please look at the pdf file BinaryTree.pdf posted under Files/Final. 1 3 4 5 What is the root? 6 7 8 How many nodes in the tree? How many leaves in the tree? 12 9 What is the height of the tree? 15 10 13 17 [Choose ] [Choose ] [Choose ] [Choose ] > > <
Consider the rooted tree shown below. Which of the following statements are true? a O h b e i с f d 9 The sub-tree rooted at the node "d" contains the nodes "d", "f" and "g". The parent of "b" is "e". The height of the tree is 2. The nodes "h", "i", "c", "f" and "g" are at the same level. The node "i" is a leaf node. The node "a" is an ancestor of the node "e". The depth of "b" is 2. The node "b" is a sibling of the node "d". The height of the tree is 3.
Construct a binary search tree from the list of the following keys using inserts: 18 2 9 6 7 4 3 20 16 17 8 12 5 4 The key 18 is the first one that will be inserted into the tree.Draw the final tree and 3 other trees to show the intermediate steps.Do an inorder traversal of the tree. What's the list you get?
- What is the number of leaf nodes in a 2-3-Tree with height k. - You are given a series of records whose keys are numbers. The records arrive in the following order : 15, 4, 21, 12, 10, 0, 9, 7, 3. Show all the steps of the construction of the Binary tree that results from inserting these records (assume that insertion preserves order). Show all the steps of the construction of the 2-3 tree that results from inserting these records.