1. Insert operation on AVL Trees 2. Delete operation on AVL Trees Question 1: For this lab, use your BST code implemented in the previous lab.In this lab, you have to create a height-balanced tree...

1. Insert operation on AVL Trees
2. Delete operation on AVL Trees
Question 1: For this lab, use your BST code implemented in the previous lab.In this lab, you have
to create a height-balanced tree class named “AVL”. Inherit the BST class publicly in your new
“AVL” class. You can add “height” variable in your existing TNode struct implementation.
Implement the following methods for AVL class:
a. A default Constructor which calls the default constructor of base class (BST class).
b. Override the insert method of base class (BST class) in your AVL class, so that the AVL tree
remains height-balanced after insertion of a new node.
c. Override the delete method of base class (BST class) in your AVL class, so that the AVL tree
remains height-balanced after deletion of a node.
d. A function “height” which returns the height of the tree. int height()const
e. A function “search” which returns a pointer to the value of the node containing the required key
b
Question 2: Now run the following main program.
int main()
{
AVL tree;
for (int i = 1; i <= 100;="">
tree.insert(i, i);
for (int i = -1; i >= -100; i--)
tree.insert(i, i);
for (int i = 150; i > 100; i--)
tree.insert(i, i);
for (int i = -150; i < -100;="">
tree.insert(i, i);
for (int i = 150; i > 100; i--)
tree.delete(i);

tree.inorderPrintKeys();
cout < endl=""><>
cout <"tree height:="">< tree.height()=""><>
int *val = tree.search(-100);
if (val != nullptr)
{
cout <"key= -100=""><>
}
val = tree.search(-151);
if (val == nullptr)
{
cout <"key= -151="" not=""><>
}
system("pause");
}
Question 3: Provide the implementation of following functions in your BST class.
1. Add a member function printCommonAncestors which is passed two keys (k1 and k2) as parmeters.
The function then prints the keys of all ancestor nodes that are common between node n1 (containing
key k1) and node n2 (containing key k2).
void printCommonAncestors(K k1, K k2) const;
2. Add a member function getTreeWidth which returns the count of number of nodes of that level that
has the maximum number of nodes. int getTreeWidth() const;
3. Add a member function kthMaxKey which is passed a positive integer (let’s call it K) as a parameter.
The function then finds the kth maximum key from the binary search tree. If the number of nodes is
less than k, then throw an exception. K kthMaxKey(int const key) const;
4. Add a member function is isCompleteBST which returns true if the binary search tree is a complete
binary search tree. A complete binary search tree is a binary search tree in which all levels, except
possibly the last level, are completely filled (they form a perfect binary tree); and the nodes in the last
level are as far left as possible. bool isCompleteBST() const;