This is something I do not quite understand. When I read literature on heaps, it always says that the big advantage of a heap is that you have the top (max if max heap) element immediately available. But couldn't you just use a BST and store a pointer to the same node (bottom-rightmost) and update the pointer with insertions/deletions?

If I'm not mistaken, with the BST implementation I'm describing you would have

```
================================================
                    | Insert    | Remove Max
================================================
 Special BST        | O(log(n)) |    O(1)
================================================
 Max Heap           | O(log(n)) |    O(log(n))
================================================

```

making it better.

Pseudo-code:

```
Insert:
   Same as regular BST insert, but can keep track of whether
   item inserted is max because traversal will be entirely
   in the right direction.

Delete
   Set parent of max equal to null. Done.

```

What am I missing here?