[Haskell-cafe] Re: Learning about Programming Languages (specifically Haskell)

[Samuel Williams]

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 ----}