module Matrix where
import Data.List  (intercalate)

data Mat a = Mat [[a]]
type Pos  = (Int, Int)

instance Functor Mat where
  fmap f (Mat m) = Mat ((map . map) f m)

instance (Show a) => Show (Mat a) where
  show (Mat m) = concatMap ((++"\n") . intercalate " " . map show) m

-- | Safely access a list
-- [4,1,5,9] ?? 2 == Just 5
-- [5,7] ?? 3 == Nothing
(??) :: [a] -> Int -> Maybe a
xs     ?? n | n < 0 =  Nothing
[]     ?? _         =  Nothing
(x:_)  ?? 0         =  Just x
(_:xs) ?? n         =  xs ?? (n-1)

-- | Create a matrix of indeces of a matrix
indeces :: Mat a -> Mat Pos
indeces (Mat m) = Mat [[(x,y) | y <- [0..length (m !! x)-1]] |
                                x <- [0..length m-1]]

-- | Create a matrix of zeros
zeros :: Int -> Int -> Mat Int
zeros x y = Mat (replicate x $ replicate y 0)