3. The sequence of keys 4, 7, 9, 11, 14, 17, 18, 19, 22 is obtained by an inorder traversal of binary search trees. (a) Please show out two different binary search trees which can produce the same sequence. (10%) (b) Given a binary search tree, please give an efficient procedure to generate the other binary search tree which has the same inorder ordering of keys. (10%) (c) If it is possible to have the third binary search tree has the same inorder ordering of keys. (10%)

3. The sequence of keys 4, 7, 9, 11, 14, 17, 18, 19, 22 is obtained by an inorder traversal of binary search trees. (a) Please show out two different binary search trees which can produce the same sequence. (10%) (b) Given a binary search tree, please give an efficient procedure to generate the other binary search tree which has the same inorder ordering of keys. (10%) (c) If it is possible to have the third binary search tree has the same inorder ordering of keys. (10%)

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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5.(b) Instructor Rafiq Ahmed stores the scores of his students in the form of Binary Search (12) Tree. The scores are 76, 55, 90, 38, 45, 83, 100, 93, 86. Find the Binary Search Tree. Find the internal nodes and the height of the tree. Write down the pre-order traversal if your student ID is odd, Post-order traversal if your student ID is even. (For example- the student with student ID 2105001 will traverse the tree in pre-order.)
Q 2. Draw the sequence of AVL trees obtained when the following keys are inserted one-by-one, in the order given into an initially empty AVL search tree: {F, E, A, B, Ď, C, G}. Identified rotations, if there is any. (10)
Refer to Binary Search Tree created in following values apply in-order traversal on BST. 3,5,32,65,8,5,3,9,0,1,2
2. Illustrates in the form of a binary search tree (ABB) the following elements: A = 49, 60, 20, 32, 65, 30, 25, 52, 18.
2. a) Suppose the tree in Figure below is an unordered tree, i.e., the order in which the children appear is not relevant. Now determine whether each of the following breadth-first traversals is valid or not. You need to justify your answer: GFBKECAINJDHMLO GFBKECAINJDHMLO GKFBIJNEACOMLHD GFBKECAINJOMLHD
P1
2. This question is about binary search tree.a. Show the final result after inserting 3, 1, 4, 6, 9, 2, 8, 5, 7, 0 into an empty binary search tree.b. Show the result of deleting the root twice. If the deleted node contains 2 children, its value is replaced by the minimum value of the right subtree, and the deletion is propagated. Show the result after each deletion
b. Given a BST whose root node is represented by the node root. Write a function findroots(Node * root) to traverse the BST and print the number of total parent (atleast have a child node) nodes of the BST. N.B: Print order doesn't matter Fig 1: An example Binary Search Tree. 5 For example: In this figure, there are total 4 parents
Create a function that checks whether a binary tree is balanced. For the sake of this issue, a balanced tree is one in which the heights of the two subtrees of each node never deviate by more than one.
Please show steps clearly
(b) (i) Define the structure of a binary tree. Explain the algorithm for inserting a number onto a binary tree such that the numbers on the tree can be traversed in a sorted manner. You do not need to explain the process of traversal. Draw the binary tree created by the algorithm when it inserts these numbers one by one from left to right: (ii) 9, –16, 8, 12, 32, 21, 4, -6, 8, 14,–2, –20, 40
a. Given the definition of a binary tree, Insert, into an empty binary search tree, entries with keys {55, 34, 19, 78, 65, 8, 22, 97, 53, 26,76, 39, 93, 69, 11 ,83,2,35,70,77} (in this order). Draw the tree after each insertion