The answer to 'but why' use the Goedel numbering scheme is:
gn(UV) = gn(U) * gn(V)
Concatenation in string-land becomes multiplication in number-land.
In other words, you need to compute the signature of each
string in the dataset exactly once. After that it's just
one multiply per test.
Your other solutions are computing the signatures of concatenated
strings about (N^2)/2 times.
The overall performance of both should be O(N^2).
-- Michael Glass
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