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 ([email protected]) 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.