careful, things don't collapse so easily; otherwise we'd always have
either O(n) or O(1).

Agreed, it is a constant, as much as traversing a bst is a constant
bound above by some fixed value. When determining runtime in big-O, you
must always use the upper bound.

Now for strings, m would be some f(max_string_length) - which in this
example is not likely to be >= n (but in many cases could be and
therefore wouldn't be negligible)

The two methods are practically the same (I agree my overlooking the
compare function in my example wasn't fair) - but the question now
becomes, which better suits the target language...

NOTE:
in m = f(max_string_length) I assume that max_string_length is the main
dependancy driving the hash function.


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