Starting Out With C++, Early Objects (Looseleaf)
8th Edition
ISBN: 9780133427622
Author: GADDIS
Publisher: PEARSON
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Chapter 19, Problem 12RQE
Program Plan Intro
Binary tree:
- Binary tree is a non-linear data structure.
- Binary tree contains node such as root node that is pointed to two child nodes.
- A root node will have left reference node and right reference node.
- Binary tree will contain more than one self-referenced field.
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Given a set of 9 letters { H, K, S, P, A, E, I, O, U }, answer the following: a) Draw a binary search tree which is also a complete binary tree, constructed with the letters of the given set above (based on alphabetical ordering). NO steps required.b) Determine and list the sequence of elements obtained by post-order traversing the binary search tree constructed above. NO steps required.c) A new letter N is first inserted into the binary search tree determined above, followed by inserting another letter M. The original letter K is then removed from the binary search tree. Draw the updated binary search tree after these insertions and removal. NO steps required.
d) Find the average search length of the updated binary search tree in step c) with 2 decimal places, assume all nodes in the tree have same probability in searching. Clearly show the steps of your calculation.
A) Suppose the numbers 7 , 5 , 1 , 8 , 3 , 6 , 0 , 9 , 4 , 2 are inserted in that order into an initially empty binary search tree. The binary search tree uses the usual ordering on natural numbers.
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A) In order
B) pre order
C) post order
a) Write a RECURSIVE function to count the number of non-leaf nodes in a general Binary Tree. A leaf node is a node with no children.
b) Now, assume you have a full binary tree with n nodes. A full binary tree is a binary tree in which all leave nodes have the same depth and all internal (non-leaf) nodes have exactly two children. Write a recurrence relation for the time complexity of your algorithm in part a once the input to your function is a full binary tree. Explain why you came up with such a recurrence relation. Then bound the relation in Big-O(). (You might use Master Theorem if applicable). Please show all work in depth for each step.
Chapter 19 Solutions
Starting Out With C++, Early Objects (Looseleaf)
Ch. 19.1 - Prob. 19.1CPCh. 19.1 - Prob. 19.2CPCh. 19.1 - Prob. 19.3CPCh. 19.1 - Prob. 19.4CPCh. 19.1 - Prob. 19.5CPCh. 19.1 - Prob. 19.6CPCh. 19.2 - Prob. 19.7CPCh. 19.2 - Prob. 19.8CPCh. 19.2 - Prob. 19.9CPCh. 19.2 - Prob. 19.10CP
Ch. 19.2 - Prob. 19.11CPCh. 19.2 - Prob. 19.12CPCh. 19 - Prob. 1RQECh. 19 - Prob. 2RQECh. 19 - Prob. 3RQECh. 19 - Prob. 4RQECh. 19 - Prob. 5RQECh. 19 - Prob. 6RQECh. 19 - Prob. 7RQECh. 19 - Prob. 8RQECh. 19 - Prob. 9RQECh. 19 - Prob. 10RQECh. 19 - Prob. 11RQECh. 19 - Prob. 12RQECh. 19 - Prob. 13RQECh. 19 - Prob. 14RQECh. 19 - Prob. 15RQECh. 19 - Prob. 16RQECh. 19 - Prob. 17RQECh. 19 - Prob. 18RQECh. 19 - Prob. 19RQECh. 19 - Prob. 20RQECh. 19 - Prob. 1PCCh. 19 - Prob. 2PCCh. 19 - Prob. 3PCCh. 19 - Prob. 4PCCh. 19 - Prob. 5PCCh. 19 - Prob. 6PCCh. 19 - Prob. 7PCCh. 19 - Prob. 8PCCh. 19 - Prob. 9PC
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Similar questions
- Write a program in c++ to do the following operations on a Binary Search Tree (BST) considering the inputs are a set of strings that represent the names of 12 months of a year (in the order of January, February, . . ., December). i) Print the successor and predecessor of any given node. ii) Search a particular string is present in the BST or not. iii) Delete any string from the BST.arrow_forwardCreate a function to determine whether a binary tree is balanced. For the sake of this inquiry, a balanced tree is one where the heights of any given node's two subtrees never vary by more than one.arrow_forwardSuppose you started with an empty binary search tree. We've seen previously that inserting the keys 1, 2, 3, 4, 5, 6, 7 (in that order) would lead to a binary search tree whose shape we called degenerate. Propose a second ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If possible, propose a third ordering of the same keys that would also lead to a degenerate-shaped binary search tree. If there are no more orderings other than the one we provided and the second one you proposed, briefly explain why there are no more.arrow_forward
- (a) Describe the structure of a complete binary tree of height h with maximum number of nodes.Derive the minimum number of nodes, n(max) (h), of this tree as a function of h.(b) Describe the structure of a complete binary tree of height h with minimum number of nodes.Derive the maximum number of nodes, n(min)(h), of this tree as a function of h.(c) Derive an expression for the height of a binary tree h in terms of the number of nodes, n.arrow_forwardCreate a function to determine whether a binary tree is balanced. A balanced tree, for the purposes of this question, is one in which the heights of the two subtrees of any node never differ by more than one.arrow_forwardImplement a function to verify if a binary tree is balanced. A balanced tree, for the purposes of this question, is one in which the heights of the two subtrees of any node never differ by more than one.arrow_forward
- write a c++ code using binary search tree to store ten names of cities, search city names in tree, remove three cities name, beside the used cities in code add two new names of cities and search those newly added cities (code consist of all of above tasks)arrow_forwardCreate a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follow: //PICTURE// You should input the nodes in pre-order sequence. If a child of a node is NULL, input a space. Write the function of create binary tree, pre-order to print the nodes, in-order to print the nodes and post-order to print the nodes. Count the height of the tree.arrow_forwardAnswer the following questions using python and without using any of its libraries or OOP . a) Using the helper function insert (bst, key), create the binary search tree that results from inserting the following keys in the order given: 68, 88, 61, 89, 94, 50, 4, 76, 66, and 82. b) Using the helper function exist (bst, key), check whether key 50 exists in resultant Binary Search Tree. c) Using the helper function exist (bst, key), check whether key 49 exists in resultant Binary Search Tree. d) Using the helper function minimum (bst, starting_node), find the node with the minimum value in resultant Binary Search Tree from starting node = 68. e) Using the helper function minimum (bst, starting_node), find the node with the minimum value in resultant Binary Search Tree from starting node = 88. f) Using the helper function maximum (bst, starting_node), find the node with the maximum value in resultant Binary Search Tree from starting node = 68. g) Using the helper function maximum (bst,…arrow_forward
- Write a program in C++ to do the following operations on a Binary Search Tree (BST) considering the inputs are a set of strings that represent the name of 12 months of a year (in the order January, February,. . ., December). i) Create a BST and add one by one string where each string represents the name of a month. ii) Print the inorder, pre-order, and post-order traversal of the BST. iii) Print the minimum and maximum value strings among all the strings after the creation of the entire BST. Here, minimum and maximum values decided based on the alphabetical order of the strings. (For, example: Among January, February and March, ‘February is minimum value of the string and ‘March’ is the maximum value of string.)arrow_forwardGiven a number and a sorted binary tree, write function that inserts the number into the tree. Given a list of numbers, write a function that inserts each number into the tree. Given a sorted tree, write a function that creates a sorted list.arrow_forwardSuppose the following list of letters is inserted in an order into an empty list binary search tree J,R,D,G,T,E,M,H,P,A,F,Q Using the insertion algorithm of binary search tree: Construct the tree. Traverse it, in in-order form. Apply searching Algorithm to find the location of node ‘F’. Mention the Number of Comparison that are made until you find location ‘F’.arrow_forward
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