(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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please draw solution. no programming
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6. Consider the following AVL Tree. 50 25 75 100 a) Insert the following values in the given AVL Tree, one after another, and show the resulting tree after each insertion. You must justify your answer by explaining the rotation operation you performed during insertion. 110 60 15 22 120 20 b) Delete the root of the resulting tree in Question 2.a. Show the resulting AVL Tree. Justify your answer by showing every step during deletion.
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