The tree is not needed to walk around the nodes.
It is however still needed for anything that requires modifying the
tree.
There is no immediate benefit in changing this API, but there might be
situations in the future where we can avoid looking up the tree when we
just want to check some details about the node.
Store a link to the tree in the root node. This allows looking up the
tree in O(log N) from the node without any extra memory usage.
This is useful because code can just store a pointer to the node and
doesn't need to keep the tree pointer around. And that can (for large
trees) save quite a bit of memory.
Searching through the tree is too specific to use a general function.
All the existing code just copies and slightly adapts the same 20 lines
instead, so there's no reason to keep the complicated API.
