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




/**
 * 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;
}