#include "AvlTree.h"    #include <iostream.h>    /**     * Implements an unbalanced Avl search tree.     * Note that all "matching" is based on the compares method.     * @author Mark Allen Weiss     */        /**         * Construct the tree.         */        template <class Comparable>        AvlTree<Comparable>::AvlTree( const Comparable & notFound ) :          ITEM_NOT_FOUND( notFound ), root( NULL )        {        }        /**         * Copy constructor.         */        template <class Comparable>        AvlTree<Comparable>::AvlTree( const AvlTree<Comparable> & rhs ) :          ITEM_NOT_FOUND( rhs.ITEM_NOT_FOUND ), root( NULL )        {           *this = rhs;        }        /**         * Destructor for the tree.         */        template <class Comparable>        AvlTree<Comparable>::~AvlTree( )        {            makeEmpty( );        }        /**         * Insert x into the tree; duplicates are ignored.         */        template <class Comparable>        void AvlTree<Comparable>::insert( const Comparable & x )        {            insert( x, root );        }        /**         * Remove x from the tree. Nothing is done if x is not found.         */        template <class Comparable>        void AvlTree<Comparable>::remove( const Comparable & x )        {            cout << "Sorry, remove unimplemented; " << x <<                 " still present" << endl;        }        /**         * Find the smallest item in the tree.         * Return smallest item or ITEM_NOT_FOUND if empty.         */        template <class Comparable>        const Comparable & AvlTree<Comparable>::findMin( ) const        {            return elementAt( findMin( root ) );        }        /**         * Find the largest item in the tree.         * Return the largest item of ITEM_NOT_FOUND if empty.         */        template <class Comparable>        const Comparable & AvlTree<Comparable>::findMax( ) const        {            return elementAt( findMax( root ) );        }        /**         * Find item x in the tree.         * Return the matching item or ITEM_NOT_FOUND if not found.         */        template <class Comparable>        const Comparable & AvlTree<Comparable>::                                 find( const Comparable & x ) const        {            return elementAt( find( x, root ) );        }        /**         * Make the tree logically empty.         */        template <class Comparable>        void AvlTree<Comparable>::makeEmpty( )        {            makeEmpty( root );        }        /**         * Test if the tree is logically empty.         * Return true if empty, false otherwise.         */        template <class Comparable>        bool AvlTree<Comparable>::isEmpty( ) const        {            return root == NULL;        }        /**         * Print the tree contents in sorted order.         */        template <class Comparable>        void AvlTree<Comparable>::printTree( ) const        {            if( isEmpty( ) )                cout << "Empty tree" << endl;            else                printTree( root );        }        /**         * Deep copy.         */        template <class Comparable>        const AvlTree<Comparable> &        AvlTree<Comparable>::        operator=( const AvlTree<Comparable> & rhs )        {            if( this != &rhs )            {                makeEmpty( );                root = clone( rhs.root );            }            return *this;        }        /**         * Internal method to get element field in node t.         * Return the element field or ITEM_NOT_FOUND if t is NULL.         */        template <class Comparable>        const Comparable & AvlTree<Comparable>::elementAt( AvlNode<Comparable> *t ) const        {            if( t == NULL )               return ITEM_NOT_FOUND;            else               return t->element;        }        /**         * Internal method to insert into a subtree.         * x is the item to insert.         * t is the node that roots the tree.         */        template <class Comparable>        void AvlTree<Comparable>::insert( const Comparable & x, AvlNode<Comparable> * & t ) const        {            if( t == NULL )                t = new AvlNode<Comparable>( x, NULL, NULL );            else if( x < t->element )            {                insert( x, t->left );                if( height( t->left ) - height( t->right ) == 2 )                    if( x < t->left->element )                        rotateWithLeftChild( t );                    else                        doubleWithLeftChild( t );            }            else if( t->element < x )            {                insert( x, t->right );                if( height( t->right ) - height( t->left ) == 2 )                    if( t->right->element < x )                        rotateWithRightChild( t );                    else                        doubleWithRightChild( t );            }            else                ;  // Duplicate; do nothing            t->height = max( height( t->left ), height( t->right ) ) + 1;        }        /**         * Internal method to find the smallest item in a subtree t.         * Return node containing the smallest item.         */        template <class Comparable>        AvlNode<Comparable> *        AvlTree<Comparable>::findMin( AvlNode<Comparable> *t ) const        {            if( t == NULL)                return t;            while( t->left != NULL )                t = t->left;            return t;        }        /**         * Internal method to find the largest item in a subtree t.         * Return node containing the largest item.         */        template <class Comparable>        AvlNode<Comparable> *        AvlTree<Comparable>::findMax( AvlNode<Comparable> *t ) const        {            if( t == NULL )                return t;            while( t->right != NULL )                t = t->right;            return t;        }        /**         * Internal method to find an item in a subtree.         * x is item to search for.         * t is the node that roots the tree.         * Return node containing the matched item.         */        template <class Comparable>        AvlNode<Comparable> *        AvlTree<Comparable>::find( const Comparable & x, AvlNode<Comparable> *t ) const        {            while( t != NULL )                if( x < t->element )                    t = t->left;                else if( t->element < x )                    t = t->right;                else                    return t;    // Match            return NULL;   // No match        }        /**         * Internal method to make subtree empty.         */        template <class Comparable>        void AvlTree<Comparable>::makeEmpty( AvlNode<Comparable> * & t ) const        {            if( t != NULL )            {                makeEmpty( t->left );                makeEmpty( t->right );                delete t;            }            t = NULL;        }        /**         * Internal method to clone subtree.         */        template <class Comparable>        AvlNode<Comparable> *        AvlTree<Comparable>::clone( AvlNode<Comparable> * t ) const        {            if( t == NULL )                return NULL;            else                return new AvlNode<Comparable>( t->element, clone( t->left ),                                              clone( t->right ), t->height );        }        /**         * Return the height of node t or -1 if NULL.         */        template <class Comparable>        int AvlTree<Comparable>::height( AvlNode<Comparable> *t ) const        {            return t == NULL ? -1 : t->height;        }        /**         * Return maximum of lhs and rhs.         */        template <class Comparable>        int AvlTree<Comparable>::max( int lhs, int rhs ) const        {            return lhs > rhs ? lhs : rhs;        }        /**         * Rotate binary tree node with left child.         * For AVL trees, this is a single rotation for case 1.         * Update heights, then set new root.         */        template <class Comparable>        void AvlTree<Comparable>::rotateWithLeftChild( AvlNode<Comparable> * & k2 ) const        {            AvlNode<Comparable> *k1 = k2->left;            k2->left = k1->right;            k1->right = k2;            k2->height = max( height( k2->left ), height( k2->right ) ) + 1;            k1->height = max( height( k1->left ), k2->height ) + 1;            k2 = k1;        }        /**         * Rotate binary tree node with right child.         * For AVL trees, this is a single rotation for case 4.         * Update heights, then set new root.         */        template <class Comparable>        void AvlTree<Comparable>::rotateWithRightChild( AvlNode<Comparable> * & k1 ) const        {            AvlNode<Comparable> *k2 = k1->right;            k1->right = k2->left;            k2->left = k1;            k1->height = max( height( k1->left ), height( k1->right ) ) + 1;            k2->height = max( height( k2->right ), k1->height ) + 1;            k1 = k2;        }        /**         * Double rotate binary tree node: first left child.         * with its right child; then node k3 with new left child.         * For AVL trees, this is a double rotation for case 2.         * Update heights, then set new root.         */        template <class Comparable>        void AvlTree<Comparable>::doubleWithLeftChild( AvlNode<Comparable> * & k3 ) const        {            rotateWithRightChild( k3->left );            rotateWithLeftChild( k3 );        }        /**         * Double rotate binary tree node: first right child.         * with its left child; then node k1 with new right child.         * For AVL trees, this is a double rotation for case 3.         * Update heights, then set new root.         */        template <class Comparable>        void AvlTree<Comparable>::doubleWithRightChild( AvlNode<Comparable> * & k1 ) const        {            rotateWithLeftChild( k1->right );            rotateWithRightChild( k1 );        }        /**         * Internal method to print a subtree in sorted order.         * t points to the node that roots the tree.         */        template <class Comparable>        void AvlTree<Comparable>::printTree( AvlNode<Comparable> *t ) const        {            if( t != NULL )            {                printTree( t->left );                cout << t->element << endl;                printTree( t->right );            }        }