Exercise 2: AVL Trees Construct AVL trees by inserting the elements successively, starting with the empty tree. a) 1, 2, 3, 4, 5, 6 b) 6, 5, 4, 3, 2, 1 c) 3, 6, 5, 1, 2, 4 (Note: Observe the final trees and you will find that although all of them have the same data, the tree are not necessarily the same.)

11. Preorder Traversal What is the preorder traversal order of the following tree: 3 Pick ONE option 1, 2, 4, 5, 3 4, 2, 5, 1, 3 4,5, 2, 3, 1 1,2, 3, 4, 5 Clear Selection

If Treel and Tree2 are the trees indicated below, B F) H Tree2 Treel which traversals of Treel and Tree2, respectively, will produce the same sequence of node names? Preorder, postorder Postorder, inorder Postorder, postorder Inorder, inorder Postorder, preorder

Please fill in the gaps and answer the questions.

True or False: Any node in a tree can be viewed as being the root of its own tree.

The constructed B+ index is shown on the figure below: X y 25 W Z P 1 10 16 23 25 31 36 45 52 61 69 Show the state of the index after each of the following operations: a) Write the missing values x,y,w,z into the initial status of the tree

Binary Trees (C++) You will create a class for Emploveelnfo that contains: • Employee ID Number – int Employee Name – string Implement a binary tree whose nodes hold an instance of your Emploveelnfo class. The nodes should be sorted on the Employee ID number. You will have a binary tree class header and implementation file. You can write your main to use the following information to test your tree: Employee Name James B W Bevis Employee ID Number 6702 Romney Wordsworth Revis Jacara Clegg Forbes Kalin Tros 1255 1071 2390 1558 7406 Archibald Beechcroft Penthor Mul Bartlet Finchley 7562 3004 4922 Latham Bine 8483 Jeff Myrtlebank Your program should read an employee ID and display a message telling the user whether it was found in the tree or not. Your main will have one binary tree object and all of the operations on the binary tree will be class methods. Other functions to add • Add function to display the tree • Allow user to add a new employee • Allow user to remove an employee NOTE –…

4. Complete the fuction definition given below that takes the root node of a tree as a parameter and returns the count of nodes. int count_nodes(Node *root){ // complete the function }

Q4: Is BST Write a function is_bst, which takes a Tree t and returns True if, and only if t is a valid binary search tree, which means that: Each node has at most two children (a leaf is automatically a valid binary search tree) The children are valid binary search trees • For every node, the entries in that node's left child are less than or equal to the label of the node • For every node, the entries in that node's right child are greater than the label of the node

Please write the echo statements without creating the trees no output? 3 echo statements.