6. Draw the result of applying R-B Tree Insertion to insert 48 in the following red-black tree. (You may represent black nodes as nodes with double circles, and red nodes as nodes with dashed circles.) Indicate which nodes are red or black in your drawing. Be sure that the resulting tree satisfies all the invariants of a red-black tree. Show your work, i.e., show the effect of each step of the insertion procedure on the tree. 10 20 25 30 33 35 38 40 O 45 O 50 55 60 69

6. Draw the result of applying R-B Tree Insertion to insert 48 in the following red-black tree. (You may represent black nodes as nodes with double circles, and red nodes as nodes with dashed circles.) Indicate which nodes are red or black in your drawing. Be sure that the resulting tree satisfies all the invariants of a red-black tree. Show your work, i.e., show the effect of each step of the insertion procedure on the tree. 10 20 25 30 33 35 38 40 O 45 O 50 55 60 69

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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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
Use any drawing application 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 and the second node(1), and so on. Don't forget to show any encountered violation while constructing the tree. In other words, indicate the case number and the needed action to treat that violation.
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…
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?
Q2. You are asked to write a method that takes a binary search tree (BST) as a parameter and returns the AVL tree obtained by rearranging the BST. The method should convert the BST into an AVL tree by using rotation operations. Explain your function in detail and give theoretical run time complexity analysis of that method in the report.
Examine a traversal of a binary tree. Let's say that visiting a node means to display the data in the node. What are the result of each of the following traversals of the tree included? It is preorder, postorder, inorder or level order?
(a)Draw updated AVL tree after deletion of 20? Draw each rotation.Insert Node 130 after step (a), then insert 125.
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.
I 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 99
c. Develop a method for locating the B-tree node with the biggest key.
Imagine 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.
2. Create a binary tree for which two given lists of n labels 0, 1,..., n - 1 are formed through the tree's inorder and postorder traversals. Additionally, your method should identify inputs for which there is no solution to the issue.