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, countHNodes(), that returns the number of H-nodes in a binary tree (pointed by p) using recursion.

Using the recursion tree method find the upper and lower bounds for the following recurrence (if they are the same, find the tight bound). T (n) = T (n/2) + 2T (n/3) + 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

Create a function that rapidly identifies whether any two nodes u and v in a tree T with s as the root node are ancestors or descendants of each other.

In the binary search tree, write a function that takes in a root, p, and checks whether the tree rooted in p is a binary search tree or not. What is the time complexity of your function? def is_bst(self, p: Node):

Let T be a binary search tree with n nodes, in which n > 0. When T is linear, the search algorithm makes key comparisons, in the unsuccassful case.

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

For a binary tree, the pre-order traversal is H D A C B G F E the in-order traversal is: A D C B H F E G (A) Draw this binary tree (B) Give the post-order traversal