A binary tree with only one node has a height of 1.Questions:1. At most how many and at least how many nodes can a binary tree of height 2016 have? Justifyyour answers.2. Write a function Height(t) that, given a treet, returns its height.3. Peter wants to check if a binary search treet is an AVL tree. Write a function ISAVL(t) thattakes a binary search tree t as input and returns TRUE if the tree is an AVL tree (balanced) andFALSE otherwise.

1. At most how many and at least how many nodes can a binary tree of height 2016 have?At most:A…

Answered: A binary tree with only one node has a…

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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7. Draw an AVL tree of height 3 with the smallest possible number of nodes. Then draw an AVL tree of height 4 with the smallest possible number of nodes. In pseudocode, write a function that returns the number of nodes in the smallest possible AVL tree of height h. You may assume that only valid heights from -1 up to 25 will be supplied. Write your solution below. function minAvlSize (int height)
The level of a node in the tree is the number of nodes in the path from the root to the node (including itself). For example, the node 15 in the example tree above has a level of 2. Write a function prune-tree that will take a tree representation as well as an integer level. It will return a new tree containing only nodes that have level not exceeding level. The order of the nodes in the result list should be the same as the original order in the tree. You may assume that level is a non-negative integer. write the program in racket
Write a C++ program to implement binary search tree (BST). Your program should accept a list ofnumbers from the user (minimum 5) and then build a binary search tree from those numbers.Implement following functions: Serach function: Number is found or not leavesCount: Returns number of leaves in binary tree inorder: Print the contents of tree using inorder traversal Note: Define three files: bst.h, bst.cpp, main.cpp to solve this problem
Create a binary linked tree, and traverse the tree by using the recursive function. The structure of the tree is as follows: //check pic// 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. Hints: Header file typedef char ElemType; typedef struct node//define the type of binary tree node { }BTnode; Source file #include <stdio.h> #include <stdlib.h> #include "tree.h" BTnode * createTree()//create the binary tree，return the root { BTnode *tnode;// tnode is the root char elem; ;//input the character //if the input is a space，set the pointer as NULL Else// if the input is not a space，generate the binary node and create its left…
1. Give a recursive algorithm in pseudocode to compute the diameter of a binary tree. Recall that diameter is defined as the number of nodes on the longest path between any two nodes in the tree. Nodes have left and right references, but nothing else. You must use the height function, defined as follows, in your solution. Your solution will return the diameter of the tree as an integer. function height (Node n) 1. if n = null 2. return -1 3. return 1 + max (height (n.left), height (n.right)) Write your solution below. function diameter (Node n)
I am to write a function that receives the root of a binary tree t and a number k and determine if the node where k is stored is the left child of its parent. if k is not in the tree, or does not have a parent, or is a right child the function should return false. Starting code: def is_left_child(t,k): parent, x = t.find(k, return_parent = True) return False
Please Help ASAP!! Both parts needed
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)
Build a Binary Search Tree with the given input order. You must show step by step process of inserting the inputs including both recursive calls and tree diagrams for each step. [ refer to the Insertitem function of Lecture 10 slides to get an idea of doing this.] N.B: Unique Input orders for each student to build the tree are given on a separate file. Write down the input order on your answer script before answering the question. You must use the assigned input order. Do not change the order. TREE INPUT: 4,1,9,3,2,5,6,8,7
Given two binary trees with head reference as T and S having at most N nodes. The task is to check if S is present as subtree in T.A subtree of a tree T1 is a tree T2 consisting of a node in T1 and all of its descendants in T1 You don't need to read input or print anything. Your task is to complete the function isSubtree() that takes root node of S and T as parameters and returns 1 if S is a subtree of T else 0. Expected Time Complexity: O(N).Expected Auxiliary Space: O(N). Constraints:1 <= Number of nodes <= 1051 <= Value of nodes <= 104
C PROGRAMMING Implement dijkstras alorithm Check that the Graph graph, and starting node, id, are valid• Create the set S containing all the networks (vertices) except the source node (you might wantto use an array for this.• Create an array to represent the table D and initialise it with the weights of the edges from thesource node, or infinity if no edge exists. You should use the constant DBL_MAX to representinfinity.• Create an array to represent the table R and initialise it with the next hops if an edge existsfrom the source, or 0 otherwise.• Then repeatedly follow the remaining rules of Dijkstra’s algorithm, updating the values in D andR until S is empty.• Each of the values required to complete the above can be found by calling the variousfunctions (get_vertices(), get_edge(), edge_destination(), edge_weight(), etc.)in the supplied graph library.• Once Dijkstra’s algorithm has run, you will need to create the routing table to be returned byallocating enough memory for the…
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