Given a binary tree, write a function to check if it is a valid binary search tree (BST). Discuss the approach you would take to validate the BST properties and handle edge cases.
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Q: 1 PLEASE QUESTION 1: (a) Draw a binary search tree (BST) after the insertion of keys: 8, 3, 2, 1,…
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Q: Given a binary tree, write a function to check if it is a valid binary search tree (BST). Discuss…
A: In this question we have to write function I'm for a binary tree to check if it is a valid binary…
Q: Write code for this question in C++ language only with proper comments and explaination.
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Q: Given a binary search tree and data of two nodes, find 'LCA' (Lowest Common Ancestor) of the given…
A: In this question, we have to code to find the Lowest Common Ancestor (LCA) of two nodes in a Binary…
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A: Ans: Code: #include<stdio.h>#include<stdlib.h> struct node{ int value; struct…
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- 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 <= 104Develop an array implementation of a binary search tree builtupon an array implementation of a binary tree by using thesimulated link strategy. Each element of the array will need tomaintain both a reference to the data element stored there and thearray positions of the left child and the right child. You also needto maintain a list of available array positions where elements havebeen removed, in order to reuse those positions.please explain You are given a collection of 1,000,000,000 books that are already sorted. They are labeled Book1, Book2, Book3, Book4 (book 1 is less than book 2, book 3 less than book 4, etc.). Your colleague says organizing these books in a binary search tree (BST) data structure will be useful for looking up books later. Your colleague begins inserting each book in order, but you are worried you will not get Log(N) lookup when inserting books in already sorted order. What will the lookup time be of a book when searching for a book? Group of answer choices a. O(log(n) b. O(n) c. O(n*log(n)) d. O(n*n)
- Given a binary search tree and data of two nodes, find 'LCA' (Lowest Common Ancestor) of the given two nodes in the BST.LCALCA of two nodes A and B is the lowest or deepest node which has both A and B as its descendants. Example:In this example, the green coloured node is the LCA to A and B.Alt TextNote:It is defined that each node is a descendant to itself, so, if there are two nodes X and Y and X has a direct connection from Y, then Y is the lowest common ancestor.Example:Alt TextNote:1. If out of 2 nodes only one node is present, return that node. 2. If both are not present, return -1.3. all the node data will be unique.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 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…What is the runtime (using big-O notation) of a search operation in a balanced binary search tree with n nodes? With example and explanationConsider a traversal of a binary tree. Suppose that visiting a node means to simply display the data in the node. What are the results of each of the following traversals of the tree in the following figures according to: a. Pre-order technique b. Post-order technique c. In-order technique A B D E F G H
- You are implementing a binary search tree class from scratch, which, in additionto insert, find, and delete, has a method getRandomNode() which returns a random node from the tree. All nodes should be equally likely to be chosen. Design and implement an algorithm for getRandomNode, and explain how you would implement the rest of the methodsRewrite the definition of the function searchNode of the class B-tree provided (bTree.h) by using a binary search. Write a C++ code to ask the user to enter a list of positive integers ending with -999, build a b- tree of order 5 using the positive integers, and display the tree contents. Also, ask the user to enter a number to search and display if the number is found in the tree. bTree.hPlease show steps clearly
- Given a binary search tree and data of two nodes, find 'LCA' (Lowest Common Ancestor) of the given two nodes in the BST.LCALCA of two nodes A and B is the lowest or deepest node which has both A and B as its descendants. Example:In this example, the green coloured node is the LCA to A and B.Alt TextNote:It is defined that each node is a descendant to itself, so, if there are two nodes X and Y and X has a direct connection from Y, then Y is the lowest common ancestor.Example:Alt TextNote:1. If out of 2 nodes only one node is present, return that node. 2. If both are not present, return -1.3. all the node data will be unique.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 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…Examine the variations between AVL Trees and Binary Search Trees. Do you think you'll be able to include efficiency operations into your discussion?