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Haskell Quiz/Numeric Maze/Solution Ninju

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I haven't yet added any optimization, because I wanted to keep the program as simple (and therefore readable) as possible, but I might add some later.

module Main where
import System.Environment
import Data.List
 
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"
          return ()
 
data Operation = AddTwo Integer | Double Integer | Halve Integer
 
valid :: Operation -> Bool
valid (Halve x) = x `mod` 2 == 0
valid _         = True
 
apply :: Operation -> Integer
apply (AddTwo x) = x + 2 
apply (Double x) = x * 2 
apply (Halve x) = x `div` 2
 
solve :: Integer -> Integer -> [Integer]
solve a b = solve' [[a]] b
            where
            solve' paths target = case find ((== target) . last) paths of
                                    Just path -> path
                                    Nothing -> solve' (concatMap buildPathsFrom paths) target
            buildPathsFrom path = [ path ++ [apply (op (last path))] | op <- [AddTwo, Double, Halve], valid (op (last path)) ]