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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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Given a binary search tree (BST), find the lowest common ancestor (LCA) of two given nodes in the BST. According to the definition of LCA: "The lowest common ancestor is defined between two nodes p and q as the lowest node in t that has both p and q as descendants (where we allow a node to be a descendant of itself)." For example, in the figure from question 1, the LCA between nodes 5 and 46 is 21. You may use the following typedef structure. The function returns the reference of the node that is considered the LCA. typedef struct node_s{ int data; struct node_s * leftchild; struct node _s * rightchild; }node_t;
Develop 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.
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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 explanation
construct a binary search tree using a set of numbers, similar to the example mentioned in the class. after constructing the BST, you need to give the pre-order traversal of the tree. Finally, you’re required to remove the root of tree. Please show me step by step how to do this!
Rewrite 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.h
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…
A Binary Search Tree (BST) can be used to efficiently implement a sorted set. It stores uniquevalues and offers an efficient membership method (contains).A binary search tree (BST) is a binary tree with the additional binary search tree property.The binary search tree property states that for every node n in the tree1. n.data is greater than the data value of all nodes in the sub-tree rooted with n.left.2. n.data is less than the data value of all nodes in the sub-tree rooted with n.right.As we are implementing a set, all data (strings) in the tree will be unique. Every node in the treewill have its own distinct string. Strings will be compared using the canonical way (as defined bythe compareTo() method in the String class).For example, the binary tree on the left (below) IS a binary search tree and the one on the rightis NOT.You will implement several methods in the BinaryTree and BST classes. The BST class mustextend the BinaryTree class. Methods that you must complete (implement or…
how to Traversing a Binary Search Tree. To demonstrate how this method works, implement a program that inserts a series of numbers into a BST.as given in figure.
When presenting a menu option to the user in the main cpp file. Asking user to input in an ID, how do I code a search method implementation where it takes that ID and search it in the binary tree and either return true if found and false if not. I am trying to steer away from using item which is attached to both (ID, username). I am trying to only take the ID input and the node pointer and traversing through the binary tree to find if the ID matches any of the nodes.