Yes, it is always possible to invert a (mathematical) regular expression. I don't know of a simple method for doing it, though. You have to convert the regex to an NFA (nondeterministic finite automaton), remove the nondeterminism to produce a DFA, switch the accepting and nonaccepting states, and then convert the DFA back to a regex. It's nasty, and it's not guaranteed to give you the "best" possible regex. Also, the DFA for this problem has 2**N+1 states, where N is the number of digits.

In the final step, converting the DFA to a regex, you have a choice as to which states you're going to prune off first. Boots111's first solution corresponds to pruning from left to right, while the second solution corresponds to working from the outside in. Extending the second solution to 10 digits would result in 252 branches in the top-level parenthesis group, and each of those branches would contain the solutions to two different 5-digit problems. Ick.

particle has a good idea of using backreferences. Those don't exist in "mathematical" regular expressions. The person who posed the problem might think of them as extended operators, in which case they wouldn't be allowed here. Not for me to say.

In reply to Re: Re: regexp golf - homework by no_slogan
in thread regexp golf - homework by Boots111

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