/**
 * 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;
}