Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 26.6, Problem 26.6.2CP
Program Plan Intro
AVL tree: It is a self-balancing binary search tree. If the tree is not balanced, the tree performs rotation operation.
LR rotation: It is called as Left Right rotation (double left rotation). The tree performs a single left rotation that is followed by a single right rotation.
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The following items are inserted into an AVL tree: 1, 2, 3, 8, and 9. How many rotations are performed in total to maintain an AVL tree?
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
For AVL tree in above, now what is the node X which causes the tree to be imbalanced with the alpha node at the root? Show inserting and balancing the tree. What type of imbalance is it?
Chapter 26 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 26.2 - Prob. 26.2.1CPCh. 26.2 - Prob. 26.2.2CPCh. 26.2 - Prob. 26.2.3CPCh. 26.3 - Prob. 26.3.1CPCh. 26.3 - Prob. 26.3.2CPCh. 26.3 - Prob. 26.3.3CPCh. 26.4 - Prob. 26.4.1CPCh. 26.4 - Prob. 26.4.2CPCh. 26.4 - Prob. 26.4.3CPCh. 26.4 - Prob. 26.4.4CP
Ch. 26.5 - Use Listing 26.2 as a template to describe the...Ch. 26.6 - Prob. 26.6.1CPCh. 26.6 - Prob. 26.6.2CPCh. 26.6 - Prob. 26.6.3CPCh. 26.6 - Prob. 26.6.4CPCh. 26.7 - Prob. 26.7.1CPCh. 26.7 - Prob. 26.7.2CPCh. 26.7 - Prob. 26.7.3CPCh. 26.7 - Prob. 26.7.4CPCh. 26.8 - Prob. 26.8.1CPCh. 26.8 - Prob. 26.8.2CPCh. 26.8 - Prob. 26.8.3CPCh. 26.9 - Prob. 26.9.1CPCh. 26.9 - Prob. 26.9.2CPCh. 26.9 - Prob. 26.9.3CPCh. 26 - Prob. 26.5PE
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- Using your registration number, Draw a binary tree and apply two rotations. Write down the pseudocode and explain how many nodes moved to make the tree as an AVL tree?arrow_forwardHow many different AVL trees can result from inserting permutations of 1, 2, and 3 into an initially empty tree?arrow_forwardBuild an AVL tree with the following values: 15, 20, 24, 10, 13, 7, 30, 36, 25arrow_forward
- Draw the tree step by step Delete From AVL tree for the following elements 9,8,12,15,18arrow_forward1.The tree is not an AVL tree because the following node(s) is/are unbalanced: 2.Which type of rotation should be performed as part of the previous node insertion to maintain an AVL tree?arrow_forwardWhat is the maximum height of a an AVL tree with p nodes?arrow_forward
- Create an AVL tree and add the following numbers to the tree to show the addition and rotations of each number step by step. (will be done on paper without code) 75, 10, 20, 27, 19, 120, 100, 88arrow_forwardSuppose a new element 50 is to be inserted to the above tree. Answer the following questions: 1) What will be the parent node for new Node 50 ? 2) If adding the new Node 50 would make the AVL Tree balanced or unbalanced? Why ?arrow_forwardAssume we have a full 4-ary tree, which contains 100 leaves. How many internal nodes are there, and how many nodes in total are there?arrow_forward
- Write solution step by step Insert the following elements in an empty AVL tree one by one: 14,17,11,7,53,4,13. Balance the tree after each insertion. Then delete the elements: 53, 11 and balance it.arrow_forwardDraw a KD Tree in the space below with these points inserted in the following order: (7,2), (6,4), (9,6), (8,1), (4,9), and (2,3). Assume the first level of the KD Tree is split along the x-axis. What point (from the KD Tree ) is the nearest neighbor of the point (1,4)?arrow_forwardShow the tree that would result from deleting 10 from the tree in Figure 1. When node merging or redistribution is needed, if both the left and right sibling nodes are available, use the left sibling node. You may omit the parts of the tree that do not change.arrow_forward
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