[Java] Implement locking mechanism using a binary tree

This is an interesting exercise: implement a locking mechanism backed by a tree structure with parent pointers where a node can be locked if and only if none of his ancestors and descendants are locked.
Have the lock testing operation run in O(1) time, while the lock and unlock operations should run in O(H) time where H is the height of the tree.

The fact that we are given the desired runtimes is the hint we need to understand how to implement this and the parent pointer is also a key element.
A lock testing operation in constant time means we are definitely tracking the information we need on the node itself.

An O(H) lock and unlock operation means we are not scanning both branches of a node AND the ancestors every time we need to check whether any of those contains an already locked node.
The way we can accomplish this then, is if we are tracking an additional piece of information in each node and increase the complexity of both operations to maintain this information updated.

If in each node we track for example the number of locked descendants in both subtrees, we would only need to test if any ancestor is locked during the lock operation before performing the lock and we would need to reduce the count of locked nodes in our ancestors during the unlock operation.

You can check my implementation on my Gist along with some test cases in BSTLockJTests.

I was a bit lazy so I reused an existing BST implementation that is not even fully balanced, but I am expanding this code and do not like rewriting too much :)