Question

IN C++:

Create sets of 1 Million integer, where no integer is repeated. Insert these numbers to an AVL tree and an R-B tree.

Using a random number generator, select 10% of the numbers in the trees and delete them.
Repeat the experiment 10 times. Report your answers in a tables

Answer 1

#include<bits/stdc++.h>
using namespace std;

// An AVL tree node
class Node
{
   public:
   int key;
   Node *left;
   Node *right;
   int height;
};

// A utility function to get maximum
// of two integers
int max(int a, int b);

// A utility function to get the
// height of the tree
int height(Node *N)
{
   if (N == NULL)
       return 0;
   return N->height;
}

// A utility function to get maximum
// of two integers
int max(int a, int b)
{
   return (a > b)? a : b;
}

/* Helper function that allocates a
new node with the given key and
NULL left and right pointers. */
Node* newNode(int key)
{
   Node* node = new Node();
   node->key = key;
   node->left = NULL;
   node->right = NULL;
   node->height = 1; // new node is initially
                   // added at leaf
   return(node);
}
Node *rightRotate(Node *y)
{
   Node *x = y->left;
   Node *T2 = x->right;

   // Perform rotation
   x->right = y;
   y->left = T2;

   // Update heights
   y->height = max(height(y->left),
                   height(y->right)) + 1;
   x->height = max(height(x->left),
                   height(x->right)) + 1;

   // Return new root
   return x;
}

// A utility function to left
// rotate subtree rooted with x
Node *leftRotate(Node *x)
{
   Node *y = x->right;
   Node *T2 = y->left;

   // Perform rotation
   y->left = x;
   x->right = T2;

   // Update heights
   x->height = max(height(x->left),     
                   height(x->right)) + 1;
   y->height = max(height(y->left),
                   height(y->right)) + 1;

   // Return new root
   return y;
}

// Get Balance factor of node N
int getBalance(Node *N)
{
   if (N == NULL)
       return 0;
   return height(N->left) - height(N->right);
}

// Recursive function to insert a key
// in the subtree rooted with node and
// returns the new root of the subtree.
Node* insert(Node* node, int key)
{
   /* 1. Perform the normal BST insertion */
   if (node == NULL)
       return(newNode(key));

   if (key < node->key)
       node->left = insert(node->left, key);
   else if (key > node->key)
       node->right = insert(node->right, key);
   else // Equal keys are not allowed in BST
       return node;

   /* 2. Update height of this ancestor node */
   node->height = 1 + max(height(node->left),
                       height(node->right));

   /* 3. Get the balance factor of this ancestor
       node to check whether this node became
       unbalanced */
   int balance = getBalance(node);

   // If this node becomes unbalanced, then
   // there are 4 cases

   // Left Left Case
   if (balance > 1 && key < node->left->key)
       return rightRotate(node);

   // Right Right Case
   if (balance < -1 && key > node->right->key)
       return leftRotate(node);

   // Left Right Case
   if (balance > 1 && key > node->left->key)
   {
       node->left = leftRotate(node->left);
       return rightRotate(node);
   }

   // Right Left Case
   if (balance < -1 && key < node->right->key)
   {
       node->right = rightRotate(node->right);
       return leftRotate(node);
   }

   /* return the (unchanged) node pointer */
   return node;
}

// A utility function to print preorder
// traversal of the tree.
// The function also prints height
// of every node
void preOrder(Node *root)
{
   if(root != NULL)
   {
       cout << root->key << " ";
       preOrder(root->left);
       preOrder(root->right);
   }
}

// Driver Code
int main()
{
   Node *root = NULL;
   root = insert(root, 10);
   root = insert(root, 20);
   root = insert(root, 30);
   root = insert(root, 40);
   root = insert(root, 50);
   root = insert(root, 25);
   cout << "Preorder traversal of the "
           "constructed AVL tree is \n";
   preOrder(root);
  
   return 0;
}