Finding permutations using regular expressions - regex

Question

I need to create a regular expression (for program in haskell) that will catch the strings containing "X" and ".", assuming that there are 4 "X" and only one ".". It cannot catch any string with other X-to-dot relations.
I have thought about something like
[X\.]{5}
But it catches also "XXXXX" or ".....", so it isn't what I need.

Answer 1

That's called permutation parsing, and while "pure" regular expressions can't parse permutations it's possible if your regex engine supports lookahead. (See this answer for an example.)
However I find the regex in the linked answer difficult to understand. It's cleaner in my opinion to use a library designed for permutation parsing, such as megaparsec.
You use the Text.Megaparsec.Perm module by building a PermParser in a quasi-Applicative style using the <||> operator, then converting it into a regular MonadParsec action using makePermParser.
So here's a parser which recognises any combination of four Xs and one .:
import Control.Applicative
import Data.Ord
import Data.List
import Text.Megaparsec
import Text.Megaparsec.Perm
fourXoneDot :: Parsec Dec String String
fourXoneDot = makePermParser $ mkFive <$$> x <||> x <||> x <||> x <||> dot
where mkFive a b c d e = [a, b, c, d, e]
x = char 'X'
dot = char '.'
I'm applying the mkFive function, which just stuffs its arguments into a five-element list, to four instances of the x parser and one dot, combined with <||>.
ghci> parse fourXoneDot "" "XXXX."
Right "XXXX."
ghci> parse fourXoneDot "" "XX.XX"
Right "XXXX."
ghci> parse fourXoneDot "" "XX.X"
Left {- ... -}
This parser always returns "XXXX." because that's the order I combined the parsers in: I'm mapping mkFive over the five parsers and it doesn't reorder its arguments. If you want the permutation parser to return its input string exactly, the trick is to track the current position within the component parsers, and then sort the output.
fourXoneDotSorted :: Parsec Dec String String
fourXoneDotSorted = makePermParser $ mkFive <$$> x <||> x <||> x <||> x <||> dot
where mkFive a b c d e = map snd $ sortBy (comparing fst) [a, b, c, d, e]
x = withPos (char 'X')
dot = withPos (char '.')
withPos = liftA2 (,) getPosition
ghci> parse fourXoneDotSorted "" "XX.XX"
Right "XX.XX"
As the megaparsec docs note, the implementation of the Text.Megaparsec.Perm module is based on Parsing Permutation Phrases; the idea is described in detail in the paper and the accompanying slides.

Answer 2

The other answers look quite complicated to me, given that there are only five strings in this language. Here's a perfectly fine and very readable regex for this:
\.XXXX|X\.XXX|XX\.XX|XXX\.X|XXXX\.

Answer 3

Are you attached to regex, or did you just end up at regex because this was a question you didn't want to try answering with applicative parsers?
Here's the simplest possible attoparsec implementation I can think of:
parseDotXs :: Parser ()
parseDotXs = do
dotXs <- count 5 (satisfy (inClass ".X"))
let (dots,xS) = span (=='.') . sort $ dotXs
if (length dots == 1) && (length xS == 4) then do
return ()
else do
fail "Mismatch between dots and Xs"
You may need to adjust slightly depending on your input type.
There are tons of fancy ways to do stuff in applicative parsing land, but there is no rule saying you can't just do things the rock-stupid simple way.

Answer 4

Try the following regex :
(?<=^| )(?=[^. ]*\.)(?=(?:[^X ]*X){4}).{5}(?=$| )
Demo here
If you have one word per string, you can simplify the regex by this one :
^(?=[^. \n]*\.)(?=(?:[^X \n]*X){4}).{5}$
Demo here