>> And by "three pointers" you're including a pointer to the parent, yes? 
> 
>   Right. (AFAIK self-balancing binary trees require the parent pointer
> at each node, and they also make things like traversing the tree using
> iterators much easier.)
> 
>> What's the flag? the red/black flag?
> 
>   Yes. Keeping the tree balanced requires some ancillary data besides
> the pointers.

Well now, there's red-black trees, AVL trees, the BWS algorithm, 
B-trees... exactly *which* self-balancing tree algorithm are we talking 
about here?

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