Hi, original author here. I did not expect so much discussion and awareness! Once again I have to stress that I wanted to make a very general pair of equations so I could compare the efficiency gains in other algorithms from the naive versions in an 'accurate' way. If anyone has any suggestions for the algorithms involved please let me know (141bytes@gmail.com) and I'll see if it's suitable to put in. I apologise in advance if I take longer than usual to reply, A levels are a ton of work!

Also I was originally going to see how this applied to traversing really large, cross machine trees so I did not consider the algorithms that mutated the tree, but thanks for making me aware of those.

Oh boy, this is great. Thanks! I was not aware of this when I wrote the article/post. I started out by wanting to make a very generalised pair of expressions for the space requirements so I had to make very little assumptions and would be able compare it to efficiency gains by other algorithms/representations.

Again thanks, I'll try to include it this week end if I have the time.

Whoops, you're right. I've fixed it. Thanks for pointing it out!

Hi, original author here. I used "perfect" trees as I wanted to generalise it to trees of other "types", not just binary trees. But yes, you are correct that it is incomplete for the broader category of binary trees.

Other types of trees can also be unbalanced :-). E.g., the classic example of DFS is maze-solving, which is usually unbalanced.