EBK DATA STRUCTURES AND ALGORITHMS IN C
4th Edition
ISBN: 9781285415017
Author: DROZDEK
Publisher: YUZU
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Suppose the following values are inserted into a binary tree, in the order given:
12, 7, 9, 10, 22, 24, 30, 18, 3, 14, 20
Draw a diagram of the resulting binary tree.
How would the values in the tree you sketched for part a be displayed in an in-order traversal?
How would the values in the tree you sketched for part a be displayed in a preorder traversal?
How would the values in the tree you sketched for part a be displayed in a post order traversal?
What is the difference between a leaf tree which carries elements in its leaf vs bintree which carries elements on each node, what is the logic?
Question 4
Write a Lisp functions for Binary Search Tree (of numbers).
(define insertTree (x tree)) returns a new tree with x inserted.
(define findInTree(x tree)) return true if x is in the tree.
Full explain this question and text typing work only
Don't copy and paste before solution
Chapter 6 Solutions
EBK DATA STRUCTURES AND ALGORITHMS IN C
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- To delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y. Answer the following regarding insertion/deletion of keys in a B-Tree: (1)…arrow_forwardTo delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y Write pseudo code for Step (2a) for function B-Tree-Delete-Key(x, k). Make…arrow_forwardTo delete a key in a B-tree: Step 1. If the key k is in node x and x is a leaf, delete the key k from x. Step 2. If the key k is in node x and x is an internal node, do the following: 2a) If the child y that precedes k in node x has at least t keys, then find the predecessor k’ of k in the sub-tree rooted at y. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2b) If y has fewer than t keys, then, symmetrically, examine the child z that follows k in node x. If z has at least t keys, then find the successor k’ of k in the subtree rooted at z. Recursively delete k’, and replace k by k’ in x. (We can find k’ and delete it in a single downward pass.) 2c) Otherwise, if both y and z have only t-1 keys, merge k and all of z into y, so that x loses both k and the pointer to z, and y now contains 2t-1 keys. Then free z and recursively delete k from y. 1) Write pseudo code for Step (1) for function B-Tree-Delete-Key(x, k). Make…arrow_forward
- a. Construct the labeled tree representing the algebraic expression(((x – 2) + 3) – (y + 2)) / ((2 – (3 + z)) * (w – 8)) b. Suppose that x = 4, y = 3, y = 2, and w = 6, evaluate the expression inPolish form notation.arrow_forwardAssume that each node in a binary tree is distinct and that you are provided both the order in which items are discovered during a preorder traversal and a postorder traversal. What are the conditions under which you can correctly reconstruct the tree structure from these two traversal orders?arrow_forwardPLease do A,B, and C Given the following tree: A.Is the tree balanced? If not, where is the tree out of balance? B.Is it a BST? If not, where is the violation of the search tree order? C.Show the order the nodes will be visited in a preorder, inorder, and postorder traversal. Be sure to clearly indicate which traversal is which.arrow_forward
- Find the Preorder, Postorder, Inorder, and Level order traversal of the tree. Assume going "up" is the left child and going "right" is the right child.arrow_forwardTrace the construction of the AVL tree that results. Show the trees and the BFs for each node. Box in the final answer.99, 88, 77, 66, 55, 44, 33, 22, 11arrow_forwardPlease draw the following:Form a binary tree with the root node holding 20, the left and right child of the node holding 20 respectively holding 75 and 43. The next level nodes hold the data 84, 90, 57 and 71 from left to right. The node holding 84 has left and right children that respectively hold 96 and 91 and the node holding 90 has a left child that holds 93.arrow_forward
- For the question...Insert the integers 1 through 7 for a red-black tree showing each step and rotation. Be sure to indicate the color of each node. Could it be shown with drawings as the answer given is hard to follow and doesn't look right.arrow_forwardGiven a binary tree and an integer S, print all the pair of nodes whose sum equals S.Note:1. Assume the given binary tree contains all unique elements.2. In a pair, print the smaller element first. Order of different pairs doesn't matter.Input format :The first line of input contains data of the nodes of the tree in level order form. The data of the nodes of the tree is separated by space. If any node does not have a left or right child, take -1 in its place. Since -1 is used as an indication whether the left or right nodes exist, therefore, it will not be a part of the data of any node.The following line of input contains an integer, that denotes the value of S.Output Format :Print each pair in a new line, as described in the task. Constraints:Time Limit: 1 secondSample Input 1:5 10 6 2 3 -1 -1 -1 -1 -1 9 -1 -115Sample Output 1:5 106 9*/.arrow_forwardWhat is the logic behind the distinction between a leaf tree, which holds elements in its leaves, and a bintree, which carries elements on each node?arrow_forward
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