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 26.6.4CP
Program Plan Intro
AVL tree: It is a self-balancing binary search tree. If the tree is not balanced, the tree performs rotation operation.
L rotation: In this type of rotation, the node moves one position left from the present position.
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For the AVL Tree what values could you insert to cause a right-left imbalance and at which node does the imbalance occur?
Please show and explain based on the tree provided.
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?
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?
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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- (a)Draw updated AVL tree after deletion of 20? Draw each rotation.Insert Node 130 after step (a), then insert 125.arrow_forwardGiven the following AVL tree, if node 83 is deleted, how many rotations are needed to obtain an AVL tree again? Draw the tree after each rotation.arrow_forwardDraw the tree step by step Delete From AVL tree for the following elements 9,8,12,15,18arrow_forward
- given a BST, you’re asked to remove a node from it. You need to show the tree after removal of the node. How to do this, with explanation to help me preparearrow_forwardFor AVL trees, make sure to check for balance after each operation and rotate if necessary before answering the question. 2 4 6 7 8 9 10 12 14 13 15 Delete 8. After deletion, what is the depth of node 4? Delete 10. After deletion, how many nodes would have to be added to the resulting tree for it to become a full binary tree?arrow_forwardPerform the necessary rotation/s to form an AVL tree. Fill in the blank spaces in the following statement based on the resulting AVL tree. (A NULL node can be indicated by the symbol 0 (ZERO).) The right child of node F is node Blank 1. Fill in the blank, read surrounding text. . The right child of node H is nodearrow_forward
- show the AVL tree that results after each of the integer keys 9, 27, 50, 15, 2, 21, and 36 are inserted, in that order, into an initially empty AVL tree. Clearly show the tree that results after each insertion, and make clear any rotations that must be performed. Rotations must be performed after each insertion (if tree becomes unbalanced). Name each rotation and specify around which node rotation takes place.arrow_forwardDraw the AVL tree after applying following operations.arrow_forwardUsing 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_forward
- How does the concept of a splay operation work in Splay Trees, and how is it used to maintain balance in the tree? Explain the amortized analysis of splay tree operations.arrow_forwardShow the intermediate and final Splay trees resulting from removing key 25 from the following Splay tree. The intermediate trees are those resulting from zig-zag or zig-zig rotations. Indicate which scenario (zig-zag or zig-zig) occurred before each intermediate tree. 50 20 55 10 30 60 15 25 40 65 35 45arrow_forwardShow the result of inserting the numbers 1 through 15 in order into an initially empty AVL tree. What do you notice about the structure, and do you expect it to hold for any sequence 1, 2, ..., 2^k-1?arrow_forward
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