[marginalia_nu]

That's not how asymptotes work.

Big O tells you that there exists some number N such that for each number m larger than N, if O(f(m)) > O(g(m)) then f(m) > g(m). In practice, N may be 10, or it may be larger than the number of atoms in the universe. It's unrelated to the number of items in your collection, but a property of the algorithm itself.

[ninepoints]

I'm not sure why what I wrote necessitated a lesson on limits and asymptotes. My point was that given that N was the size of your tree, more often than not, big-O analysis would apply in this case since N is likely big compared to secondary fixed effects.