Haskell Quiz/Numeric Maze/Solution Ninju

module Main where
import System.Environment
import Data.List

data Operator = AddTwo | Double | Halve

main :: IO ()
main = do args <- getArgs
          if length args == 2
            then do let [a,b] = map read args
                    putStrLn $ show $ solve a b 
            else putStrLn "Usage: solve START TARGET"

apply :: Operator -> Integer -> Integer 
apply AddTwo x = x + 2 
apply Double x = x * 2 
apply Halve x = x `div` 2

valid :: Operator -> Integer -> Bool 
valid Halve x = x `mod` 2 == 0
valid _ _ = True

solve :: Integer -> Integer -> [Integer]
solve a b = solve' [[a]] b [a] 

solve' :: [[Integer]] -> Integer -> [Integer] -> [Integer]
solve' paths target seen =  case find ((== target) . last) paths of
                                Just path -> path
                                Nothing -> let newPaths = filter ((`notElem` seen) . last) $ concatMap buildPathsFrom paths
                                               newSeen = seen ++ map last newPaths
                                           in solve' newPaths target newSeen
    

buildPathsFrom :: [Integer] -> [[Integer]] 
buildPathsFrom path = let n = last path
                      in [ path ++ [ apply operator n ] | operator <- [AddTwo, Double, Halve], valid operator n ]