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 26.4, Problem 26.4.1CP
Program Plan Intro
Adelson-Velskii and Landis (AVL) tree:
- Adelson-Velskii and Landis tree is a well-balanced binary tree which is named after scientists G. M. Adelson-Velsky and E. M. Landis.
- In this tree, the difference between the heights of two different sub trees for every node may be 0 or 1.
- The process of insertion and deletion of an element in an AVL tree is same as in binary search tree except the concept of rebalancing the tree again after insertion and deletion.
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Students have asked these similar questions
Given 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.
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?
Perform 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 node
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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Similar questions
- 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?arrow_forwardRefer to the tree on the picture and answer the following questions 1. What rotation/s must be performed to make the tree balanced?2. After balancing the tree, what node will be the parent of node 71?arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Don't submit random answer. Computer science. You are given a tree — associated undirected chart without cycles. One vertex of the tree is exceptional, and you need to track down which one. You can pose inquiries in the accompanying structure: given an edge of the tree, which endpoint is nearer to the uncommon vertex, which means which endpoint's most brief way to the extraordinary vertex contains less edges. You need to track down the uncommon vertex by posing the base number of inquiries in the most pessimistic scenario for a given tree. If it's not too much trouble, note that the exceptional vertex probably won't be fixed by the interactor ahead of time: it may change the vertex to some other one, with the prerequisite of being steady with the recently offered responses. Input You are given an integer n (2≤n≤100) — the number of vertices in a tree. The folloiwing n−1 lines contain two integers every, u and v…arrow_forward
- For the AVL Tree what values could you insert to cause a right-right imbalance and at which node does the imbalance occur? Please show and explain based on the tree provided.arrow_forwardFor 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.arrow_forwardCan you form the tree in this way?arrow_forward
- Create an AVL tree with a height of 3 where the root of the tree would be the imbalanced alpha node if another single node X is inserted into the tree. Show the creation of the tree starting with the empty tree. Show each individual step of inserting the nodes and at each step state which rotation was done (if a rotation was done). Each value in the tree must be an integer and unique. For this problem, you can use drawings and even the visualization tools. You don’t need to implement this problem.arrow_forwardGiven an AVL tree, can you always build the same tree by only using BST insert operations, i.e. by not performing any rotations?arrow_forwardDraw the AVL tree after applying following operations.arrow_forward
- Draw the tree step by step Delete From AVL tree for the following elements 9,8,12,15,18arrow_forwardCorrect answer will be upvoted else Multiple Downvoted. Computer science. You are given n chains of lengths l1,l2,… ,ln. You intend to fabricate a tree utilizing some of them. Every vertex of the tree is either white or dark. The tree at first just has a white root vertex. All chains at first comprise just of white vertices. You can take one of the chains and interface any of its vertices to any white vertex of the tree with an edge. The chain turns out to be important for the tree. The two endpoints of this edge become dark. Each chain can be utilized close to once. A few chains can be left unused. The distance between two vertices of the tree is the number of edges on the most brief way between them. Assuming there is essentially k white vertices in the subsequent tree, the worth of the tree is the distance between the root and the k-th nearest white vertex. What's the base worth of the tree you can get? In case it is absolutely impossible to construct…arrow_forwardShow the structure of the Splay Tree below after searching for 2arrow_forward
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