Project Euler 118 (4m 46s)

pr118.hs

import Data.List.Split (splitPlaces)
import Data.List (permutations, sort, nub)
import Data.Numbers.Primes
import Data.Bits
import Data.Digits
import Data.Char (digitToInt)

listToNum :: [Int] -> Integer
listToNum = toInteger . foldl1 ((+).(*10))

numToList :: Integer -> [Int]
numToList = map digitToInt . show

splits :: [Int] -> [[[Int]]]
splits list = [list] : map (flip splitPlaces list . toLengths v) [1..v]
    where v = 2 ^ (length list - 1) - 1

toLengths :: Int -> Int -> [Int]
toLengths m x = helper 1 0 []
  where
    helper :: Int -> Int -> [Int] -> [Int]
    helper t l ls
      | m < t        = l+1 : ls
      | x .&. t == t = helper (t*2) 0 (l+1 : ls)
      | otherwise    = helper (t*2) (l+1) ls

main = print . length . nub . map sort . concat . filter (not . null) . map ( filter (all isPrime) . map (map listToNum) . splits ) . permutations $ [1..9]