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 26.6.1CP
Program Plan Intro
AVL tree: It is a self-balancing binary search tree. If the tree is not balanced, the tree performs rotation operation.
RR rotation: It is called as double Right rotation. The tree performs a single right rotation that is again followed by a single right rotation.
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Students have asked these similar questions
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.
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 prepare
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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Similar questions
- Please help me insert these into a red black tree. Please show it in steps and specify the rotations. I do NOT NEED THE CODE. Just the tree in a step-by-step. Thank you!arrow_forward(a)Draw updated AVL tree after deletion of 20? Draw each rotation.Insert Node 130 after step (a), then insert 125.arrow_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_forward
- 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 nodearrow_forwardI really need help with this below, please. I need to draw four AVL tree, balancing as I add items Every time I need to rebalance the tree, I must label it to show• which of the 4 cases it is (right/right, right/left, left/right, or left/left),• which rotations (left or right) are performed. If a single rebalancing operation requires two rotations, you may either show the end result after bothrotations, or show both rotations separately. Every time thr tree is rebalanced, you should draw the resulting tree in black, and draw the newly-addednodes (up to the next rebalancing) in a different color. Exercise – random orderAdd the numbers below to a balanced BST in the order given. 36 21 70 20 14 88 96 7481 19 83 68 93 16 64 99arrow_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
- Show 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_forwardHow many different AVL trees can result from inserting permutations of 1, 2, and 3 into an initially empty tree?arrow_forwardshow 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_forward
- Correct 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_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_forwardImagine that the following operations are performed on an initially empty splay tree: Insert(10), Insert(1), Insert (7), Insert (4), Insert (5), Insert (13), Find (4). Show the state of the splay tree after performing each of the above operations. Be sure to label each of your trees with what operations you have just completed.arrow_forward
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