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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).
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.