How do I use CRTP to model a AVL/BST C++ inheritance problem ?

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C++

polymorphism

Hi, what Im trying to do is to create a class AVL which will inherite from a BST class. The BST may look like :

class BST
{
private:
    struct Node
    {
        int val;
        Node* left;
        Node* right;
    };
public:
    Node* insert(Node* node) {/* do stuff using BST::Node */}

    // ...
};

So, there will be a AVL class which will inherite from BST. So far we known, AVL Node is different from BST Node, so AVL Node will be like this :

struct Node // AVL
{
    int val, height;
    Node* parent;
    Node* left;
    Node* right;
};

So now, AVL class inherite from BST class, but when I insert in a AVL, all the insertion stuff will still using BST::Node. What I want is that I can use BST as a generic algorithm to do the common stuff(since AVL and BST are very similar). But I dont known how to make BST use AVL::Node to do the common insertion stuff. I'm learning about CRTP but I dont known how to solve the problem in a elegant way. Can someone help ? (I know CRTP would be overkill for this problem, but Im trying to better understand this pattern of problem).

attachment : http://stackoverflow.com/questions/33919516/inheritance-and-avl-bst-trees/33920331#33920331[^]