AVL Tree Rotation

bool avl_search_tree::avl_tree_node::rotate_left()
{
    if (_right_child != NULL) {
        avl_tree_node *new_root = _right_child;

        if (_parent != NULL) {
            if (_parent->_left_child == this) {
                _parent->_left_child = new_root;
            } else {
                _parent->_right_child = new_root;
            }
        }

        new_root->_parent = _parent;
        _parent = new_root;

        _right_child = new_root->_left_child;
        new_root->_left_child = this;

        if (_right_child != NULL) {
            _right_child->_parent = this;
        }

        //update heights
        update_height();
        new_root->update_height();

        return true;
    }

    return false;
}