What is the definition for the height of a tree?

Question

I can't seem to find a definitive answer for this, I'm trying to do some elementary proofs on heaps but here's what's throwing me off a little bit:

Is an empty tree valid? If so, what is its height?
I would think this would be 0.

What is the height of a tree with a single node?
I would think this would be 1 but I have seen definitions where it is 0 (and if this is the case then I don't know how to account for an empty tree).

Answer 1

Height of a tree is the length of the path from root of that tree to its farthest node (i.e. leaf node farthest from the root).

A tree with only root node has height 0 and a tree with zero nodes would be considered as empty. An empty tree has height of -1. Please check this.

I hope this helps.

Answer 2

I think you should take a look at the Dictionary of Algorithms and Data Structures at the NIST website. There definition for height says a single node is height 0.

The definition of a valid tree does include an empty structure. The site doesn't mention the height of such a tree, but based on the definition of the height, it should also be 0.