Write a program named ProblemA.cpp that implements the followingfunctions using recursion. Make a menu-based implementation so that you can call each function basedon the user input. • insert: insert a new node in the BSTNode* insert (Node* root, int key); • print: prints the values of all items in the tree, using inorder traversal techniquevoid inorder (Node* root); • search: search a node with a value in the BSTNode* insert (Node* root, int key); • findMinimum: returns the element with the minimum value in the BSTNode* findMinimum (Node* root); • findMaximum: returns the element with the maximum value in the BSTNode* findMaximum (Node* root); • delete: delete a node from the BSTNode* delete (Node* root, int key);

Assume there is a rooted tree A. Write a recursive program that returns both the number of nodes(N) and number of edges(E) in A.

IN C++ please Given an infix expression, write a program to store it in an expression tree. Your program should do the following: Read any infix expression from the standard input with operators +, -, *, /, ++, --, (, and ) and construct the tree. Show the expression in prefix and postfix notation based on user choice. Return the height of the tree and the height of any node ni upon a request.

Given a binary tree, let an H-node be defined as a non-leaf node in the tree whose value is greater than or equal to its children nodes (1 or 2 children).  Write a function called countHNodes(TreeNode* p), that returns the number of H-nodes in a binary tree (pointed by p). Use recursion in the function.

Help me in C++ please:  Write a program (in main.cpp) to do the following: a. Build a binary search tree T1. b. Do a postorder traversal of T1 and, while doing the postorder traversal, insert the nodes into a second binary search tree T2 . c. Do a preorder traversal of T2 and, while doing the preorder traversal, insert the node into a third binary search tree T3. d. Do an inorder traversal of T3. e. Output the heights and the number of leaves in each of the three binary search trees. The program should accept input and produce output similar to the example below: Enter numbers ending with -999: 10 5 7 -999 tree1 nodes in postorder: 7 5 10 tree2 nodes in preorder: 7 5 10 tree3 nodes in inorder: 5 7 10 tree1 height: 3 tree1 leaves: 1 tree2 height: 2 tree2 leaves: 2 tree3 height: 2 tree3 leaves: 2 The program has 3 tabs: main.cpp , binarysearchTree.h , and binaryTree.h

B. Recall your implementation of a binary search tree. Write a function int levelOf(int k) that computes and returns the level of the node with the key k. (Consider the root at level 1)

Java.Given a binary tree, write a function that prints the binary search tree’s nodes level by level, for example the following tree will have the following output statement:1, 2, 3, 4, 5

Write a program in C++, to create a tree by using nodes, that represent the following family hierarchy. A is the father of K and L K is the father of P and Q L is the father of B and C P has only one child, i.e., J Q has no child B is the father X and Y C has only one child, i.e., Z.

Construct a Binary Search Tree (BST) using the data provided in shaded row and name it “BST-1”.                                                                                                                                                                50 45 65 60 75 90 15 35 70 45 55 40 20 80 95 85 25 50 74 5 Provide answers to the following considering your constructed BST-1: Write a C++ code for the in-order traversal of BST-1. Also, dry run your code on it and elaborate its each step. Compute the total number of used and unused (null) references defined in BST-1. And construct an equivalent two-way in-order threaded BST-1 that has minimum number of null references.