Thanks Roel and Kyle for your contributions!
On 4/05/2010, at 10:35 PM, Roel van Dijk wrote:
> Here is my attempt. I tried to avoid higher concepts like folds and
> things like the ($) operator. Most recursions are written explicitly.
>
> {---- BEGIN CODE ----}
>
> module Main where
>
> -- Data type representing a door which is either Open or Closed.
> data Door = Open | Closed deriving Show
>
> toggle :: Door -> Door
> toggle Open = Closed
> toggle Closed = Open
>
> -- Applies the function f to every n'th element of a list.
> skipMap :: (a -> a) -> Int -> [a] -> [a]
> skipMap f n | n < 1 = error "skipMap: step < 1"
> | otherwise = go (n - 1)
> where
> -- Apply the function 'f' to an element of the list when the
> -- counter reaches 0, otherwise leave the element untouched.
> go _ [] = []
> go 0 (x:xs) = f x : go (n - 1) xs
> go c (x:xs) = x : go (c - 1) xs
>
> -- Calculate the final answer.
> run :: Int -> [Door]
> run n = go 1 initialDoors -- Start by toggling every door.
> where
> -- Initial list of closed doors
> initialDoors :: [Door]
> initialDoors = replicate n Closed
>
> -- Toggle every c doors, then proceed by toggling every c+1 doors
> -- of the result, etcetera... Stops after toggling the n'th door.
> go :: Int -> [Door] -> [Door]
> go c doors
> | c > n = doors
> | otherwise = go (c + 1) (skipMap toggle c doors)
>
> -- Print information about a single door.
> printDoor :: (Int, Door) -> IO ()
> printDoor (n, door) = putStrLn ("Door #" ++ show n ++ " is " ++ show door)
>
> printRun :: Int -> IO ()
> printRun n = mapM_ printDoor (zip [1..n] (run n))
>
> -- The program entry point.
> main :: IO ()
> main = printRun 100
>
> {---- END CODE ----}
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