Question

What’s a regular expression that validates if a string is pandigital (containing all digits from 1 to 9 exactly once)?

For example:

123456789 891364572 

But not:

11234556789 25896471 

I know how to do this without regex but I was unable to form a regex for it.

Thanks.

This is not homework.

Answer 1

Short and sweet, using a negative lookahead:

/^(?!.*([1-9]).*\1)[1-9]{9}$/ 

• [1-9] is the character class for nonzero digits – equivalent to [123456789]
• .* matches any string of any length.
• .*([1-9]).*\1.* matches any string with that contains at least two occurrences of the same nonzero digit
  • a nonzero digit is matched and captured by ([1-9])
  • a repeat of that nonzero digit is matched by \1, a back-reference to the first captured match.
  • the .* matches the arbitrary padding before, and between the nonzero digit and its repeat.
• (?!<pattern>) matches any position where the contained pattern doesn’t match. This is a negative lookahead, as it only matches a position in the string, and doesn’t consume any of it – just looks ahead to compare it with the contained pattern.
• [1-9]{9} matches nine nonzeo digits.
  • <pattern>{9} means match the preceding pattern 9 times.
• ^<pattern>$ matches any string that exactly matches the contained pattern (rather than contains a substring that matches the pattern)
  • ^ matches the position at the beginning of a string OR the beginning of a line
  • $ matches the position at the end of a string OR the end of a line

So combined, we check to make sure that it’s not repeating any digits, then we check that it’s only digits. Since it’s 9 digits long, and none repeat, all must show up exactly once. That’s the pigeonhole principle at work!

The syntax for your specific regular expression engine may vary. The above is a PCRE (supported in Perl, Ruby, and a bunch of different other languages). Posix regular expressions have slightly different syntax. Not all engines support negative lookaheads, but most support back-references. Neither are part of the definition of formal theoretic regular expressions, but are very convenient.