Solution to Is a binary tree red black?

This will be a quick (and incomplete) post. I might edit to add more details later.

The goal was to determine if a given binary tree is a red black tree.

A well known necessary condition of a red-black tree: For each node the max height is no more than twice the min height.

This is in fact used to prove that the height is $O(\log n)$.

In fact, this is also sufficient!

Using this property gives us an easy $O(n)$ time algorithm.

I will leave the details of the proof and the algorithm to you :-).