#include "AATree.h"
    #include <iostream.h>

        /**
         * Construct the tree.
         */
        template <class Comparable>
        AATree<Comparable>::AATree( const Comparable & notFound ) :
          ITEM_NOT_FOUND( notFound )
        {
            nullNode = new AANode<Comparable>;
            nullNode->left = nullNode->right = nullNode;
            nullNode->level = 0;
            root = nullNode;
        }

        /**
         * Copy constructor.
         */
        template <class Comparable>
        AATree<Comparable>::AATree( const AATree<Comparable> & rhs ) :
          ITEM_NOT_FOUND( rhs.ITEM_NOT_FOUND )
        {
            nullNode = new AANode<Comparable>;
            nullNode->left = nullNode->right = nullNode;
            nullNode->level = 0;
            root = clone( rhs.root );
        }

        /**
         * Destructor for the tree.
         */
        template <class Comparable>
        AATree<Comparable>::~AATree( )
        {
            makeEmpty( );
            delete nullNode;
        }

        /**
         * Insert x into the tree; duplicates are ignored.
         */
        template <class Comparable>
        void AATree<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 AATree<Comparable>::remove( const Comparable & x )
        {
            remove( x, root );
        }

        /**
         * Find the smallest item in the tree.
         * Return smallest item or ITEM_NOT_FOUND if empty.
         */
        template <class Comparable>
        const Comparable & AATree<Comparable>::findMin( ) const
        {
            if( isEmpty( ) )
                return ITEM_NOT_FOUND;

            AANode<Comparable> *ptr = root;
            while( ptr->left != nullNode )
                ptr = ptr->left;

            return ptr->element;
        }

        /**
         * Find the largest item in the tree.
         * Return the largest item of ITEM_NOT_FOUND if empty.
         */
        template <class Comparable>
        const Comparable & AATree<Comparable>::findMax( ) const
        {
            if( isEmpty( ) )
                return ITEM_NOT_FOUND;

            AANode<Comparable> *ptr = root;
            while( ptr->right != nullNode )
                ptr = ptr->right;

            return ptr->element;
        }

        /**
         * Find item x in the tree.
         * Return the matching item or ITEM_NOT_FOUND if not found.
         */
        template <class Comparable>
        const Comparable & AATree<Comparable>::
        find( const Comparable & x ) const
        {
            AANode<Comparable> *current = root;
            nullNode->element = x;

            for( ; ; )
            {
                if( x < current->element )
                    current = current->left;
                else if( current->element < x )
                    current = current->right;
                else if( current != nullNode )
                    return current->element;
                else
                    return ITEM_NOT_FOUND;
            }
        }

        /**
         * Make the tree logically empty.
         */
        template <class Comparable>
        void AATree<Comparable>::makeEmpty( )
        {
            makeEmpty( root );
        }

        /**
         * Test if the tree is logically empty.
         * Return true if empty, false otherwise.
         */
        template <class Comparable>
        bool AATree<Comparable>::isEmpty( ) const
        {
            return root == nullNode;
        }

        /**
         * Print the tree contents in sorted order.
         */
        template <class Comparable>
        void AATree<Comparable>::printTree( ) const
        {
            if( root == nullNode )
                cout << "Empty tree" << endl;
            else
                printTree( root );
        }

        /**
         * Deep copy.
         */
        template <class Comparable>
        const AATree<Comparable> &
        AATree<Comparable>::operator=( const AATree<Comparable> & rhs )
        {
            if( this != &rhs )
            {
                makeEmpty( );
                root = clone( rhs.root );
            }

            return *this;
        }

        /**
         * Internal method to insert into a subtree.
         * x is the item to insert.
         * t is the node that roots the tree.
         * Set the new root.
         */
        template <class Comparable>
        void AATree<Comparable>::
        insert( const Comparable & x, AANode<Comparable> * & t )
        {
            if( t == nullNode )
                t = new AANode<Comparable>( x, nullNode, nullNode );
            else if( x < t->element )
                insert( x, t->left );
            else if( t->element < x )
                insert( x, t->right );
            else
                return;  // Duplicate; do nothing

            skew( t );
            split( t );
        }

        /**
         * Internal method to remove from a subtree.
         * x is the item to remove.
         * t is the node that roots the tree.
         * Set the new root.
         */
        template <class Comparable>
        void AATree<Comparable>::
        remove( const Comparable & x, AANode<Comparable> * & t )
        {
            static AANode<Comparable> *lastNode, *deletedNode = nullNode;

            if( t != nullNode )
            {
                // Step 1: Search down the tree and set lastNode and deletedNode
                lastNode = t;
                if( x < t->element )
                    remove( x, t->left );
                else
                {
                    deletedNode = t;
                    remove( x, t->right );
                }

                // Step 2: If at the bottom of the tree and
                //         x is present, we remove it
                if( t == lastNode )
                {
                    if( deletedNode == nullNode || x != deletedNode->element )
                        return;   // Item not found; do nothing
                    deletedNode->element = t->element;
                    deletedNode = nullNode;
                    t = t->right;
                    delete lastNode;
                }

                // Step 3: Otherwise, we are not at the bottom; rebalance
                else
                    if( t->left->level < t->level - 1 ||
                        t->right->level < t->level - 1 )
                    {
                        if( t->right->level > --t->level )
                            t->right->level = t->level;
                        skew( t );
                        skew( t->right );
                        skew( t->right->right );
                        split( t );
                        split( t->right );
                    }
            }
        }

        /**
         * Internal method to make subtree empty.
         */
        template <class Comparable>
        void AATree<Comparable>::makeEmpty( AANode<Comparable> * & t )
        {
            if( t != nullNode )
            {
                makeEmpty( t->left );
                makeEmpty( t->right );
                delete t;
            }
            t = nullNode;
        }

        /**
         * Internal method to print a subtree in sorted order.
         * @param t the node that roots the tree.
         */
        template <class Comparable>
        void AATree<Comparable>::printTree( AANode<Comparable> *t ) const
        {
            if( t != nullNode )
            {
                printTree( t->left );
                cout << t->element << endl;
                printTree( t->right );
            }
        }


        /**
         * Rotate binary tree node with left child.
         */
        template <class Comparable>
        void AATree<Comparable>::rotateWithLeftChild( AANode<Comparable> * & k2 ) const
        {
            AANode<Comparable> *k1 = k2->left;
            k2->left = k1->right;
            k1->right = k2;
            k2 = k1;
        }

        /**
         * Rotate binary tree node with right child.
         */
        template <class Comparable>
        void AATree<Comparable>::rotateWithRightChild( AANode<Comparable> * & k1 ) const
        {
            AANode<Comparable> *k2 = k1->right;
            k1->right = k2->left;
            k2->left = k1;
            k1 = k2;
        }

        /**
         * Skew primitive for AA-trees.
         * t is the node that roots the tree.
         */
        template <class Comparable>
        void AATree<Comparable>::skew( AANode<Comparable> * & t ) const
        {
            if( t->left->level == t->level )
                rotateWithLeftChild( t );
        }

        /**
         * Split primitive for AA-trees.
         * t is the node that roots the tree.
         */
        template <class Comparable>
        void AATree<Comparable>::split( AANode<Comparable> * & t ) const
        {
            if( t->right->right->level == t->level )
            {
                rotateWithRightChild( t );
                t->level++;
            }
        }

        /**
         * Internal method to clone subtree.
         */
        template <class Comparable>
        AANode<Comparable> *
        AATree<Comparable>::clone( AANode<Comparable> * t ) const
        {
            if( t == t->left )  // Cannot test against nullNode!!!
                return nullNode;
            else
                return new AANode<Comparable>( t->element, clone( t->left ),
                                               clone( t->right ), t->level );
        }