(a) Given the following AVL tree T: 37 24 48 30 42 60 38 89 We will insert several keys into T. For cach part of this question, show ALL steps for cach insertion, including the trees after each appropriate rotation and the resulting trees after each insertion. (i) Based on the given AVL tree, insert 40 into the AVL tree. (ii) Based on the AVL tree in (i), insert 99 into the AVL tree. (iii) Based on the AVL tree in (ii), insert 45 into the AVL tree. (b) Is the array with values [1,3,7,9,10,21,13,44,99,10,10,20] a min-hean? If yes, explain why. If no, state clearly ALL the index(s) of the array element(s) that make(s) the array not a min-heap. (c) Draw the resulting tree and array after calling max_heapify(input=a, index=0) on the array a=[1,12,11,5,6,9,8,4,3,2,0] where the function would heapify the input array from the index. Note that the function max_heapify assumes the index of the first element is 0.

(a) Given the following AVL tree T: 37 24 48 30 42 60 38 89 We will insert several keys into T. For cach part of this question, show ALL steps for cach insertion, including the trees after each appropriate rotation and the resulting trees after each insertion. (i) Based on the given AVL tree, insert 40 into the AVL tree. (ii) Based on the AVL tree in (i), insert 99 into the AVL tree. (iii) Based on the AVL tree in (ii), insert 45 into the AVL tree. (b) Is the array with values [1,3,7,9,10,21,13,44,99,10,10,20] a min-hean? If yes, explain why. If no, state clearly ALL the index(s) of the array element(s) that make(s) the array not a min-heap. (c) Draw the resulting tree and array after calling max_heapify(input=a, index=0) on the array a=[1,12,11,5,6,9,8,4,3,2,0] where the function would heapify the input array from the index. Note that the function max_heapify assumes the index of the first element is 0.

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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Similar questions

For 2-3 Trees insert 6, 3, 2, 8, 7, 9, 10 in order given into the following trees. Initially, a tree contains only a root node with two values 1 and 4. Show the snapshot of the tree after insertion.
Draw the AVL tree after applying following operations.
Use the given AVL tree to answer each of the following questions: (a) Which is the deepest unbalanced node after inserting key 5, but before re-balancing, and what is its balance factor? (b) After the insertion, perform all the necessary rotations required to re-balance the tree, and after each rotation,state the type of rotation done and list the keys of the resulting tree in the form: After Left/Right rotation: e1, e2, e3, ...., en.
The keys 24, 39, 31, 46, 48, 34, 19, 5, and 29 are inserted (in the order given) into an initially empty AVL tree. Show the AVL tree after each insertion.
Use the given AVL tree to answer each of the following questions: (a) Which is the deepest unbalanced node after inserting key 5, but before re-balancing, and what is its balance factor? (b) After the insertion, perform all the necessary rotations required to re-balance the tree, and after each rotation, state the type of rotation done and list the keys of the resulting tree in the form: After Left/Right rotation: e1, e2, e3, ...., en. (breadth-first order)
1. Answer the following with respect to red-black trees. a. Show the red-black trees that result after successively inserting the keys 41, 38, 31, 12, 19, 8 into an initially empty red-black tree. Now show the red-black trees that result from the successive deletion of the keys in the order 8, 12, 19, 31, 38, 41. b. Show the red-black trees that result after successively inserting the keys 41, 38, 31, 12, 19, 8 into an initially empty red-black tree. c. Show that the longest simple path from a node x in a red-black tree to a descendant leaf has length at most twice that of the shortest simple path from node x to a descendant leaf. d. Suppose that a node x is inserted into a red-black tree and then is immediately deleted from the tree. Is the resulting red-black tree the same as the initial red-black tree? Justify your answer. e. What is the largest possible number of internal nodes in a red-black tree with black-height k? What is the smallest possible number?
An AVL tree is constructed by inserting the following sequence of elements into empty AVL tree. After building AVL tree, if an element 14 is deleted from it, then number of levels present in AVL tree is__ (Assume root is at 1 level) 17, 14, 19, 16, 18, 15, 12, 13
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?
2. (a) Draw all binary trees with n nodes that satisfy the balance requirement of A VL trees. Assumen=1,2,3,4,5.(b) Draw a binary tree of height 4 which will also be an A VL tree (here, define height of leaf node= 0, and height of root node = 4), and which has the smallest number of nodes among all such trees
Consider an AVL-Tree of positive integers in which duplicate values are not permitted. A double rotation is triggered when the number 10 is inserted into a minimum AVL-tree of height 3. Prior and then after the insert, draw a schematic of the tree.
Q-No.2: Consider the following binary tree: iii. Delete nodes 80 and 58 in that order. Redraw the binary tree after each deletion. iv. The In-order and Pre-order series of binary tree are as follows, draw its binary tree. In-order: CEDFBAHJIKGMLPre-order: ABCDEFGHIJKLM (Sibject :Data stracture and algorithm )
Remove 5 from the following AVL tree; draw the results: