/**
 * 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 );
}