Spec.hs

import           Data.List       (permutations, sortBy)
import           Test.QuickCheck

readInt :: String -> Int
readInt = read

comp GT _ _ _ = GT
comp LT _ _ _ = LT
comp EQ _ [] [] = EQ
comp EQ previous [x] [] = compare x previous
comp EQ previous [] [y] = compare previous y
comp EQ _ (x:xs) (y:ys) = comp (compare x y) (max x y) xs ys

biggest :: [Int] -> String
biggest = concat . sortBy (flip $ comp EQ '0') . map show



bruteForce :: [Int] -> Int
bruteForce ns = maximum $ map (readInt . concat) $ permutations numbers
    where
        numbers = map show ns

prop_biggest :: NonEmptyList (NonNegative Int) -> Bool
prop_biggest (NonEmpty ns) = read (biggest numbers) == bruteForce numbers
    where
        numbers = map (\(NonNegative x) -> x) ns

main :: IO ()
main = quickCheck $ property prop_biggest