Suppose also that my faulty implementation of my faulty algorithm will give the proper output on all input.

Question:
Does my program have a bug ?

Strike outs are mine, of course.

My answer: No (with a caveat.)

Your Perl error has simply resulted in a correct algorithm. Since you've stipulated it is valid Perl then, no, there is no bug. Someone else could come along, read the code, and explain how it works.

It is possible that you've created an obfuscated solution but it is not necessarily so. It might be perfectly obvious that your algorithm works and how.

The caveat: by "valid Perl program" I assume that also means that you have not introduced any undefined behavior. Something like $b = ++$a - $a++; is valid syntax but is undefined. If your implementation contains anything of the sort, then it does have a bug. And a nasty (but latent) one at that. Upgrade Perl or change platforms and it might bite you.

Otherwise though, you've got a perfectly fine algorithm and a confused programmer... A relatively common situation, I might add! :-)

-sauoq
"My two cents aren't worth a dime.";