module Matrix where

import Control.Applicative
import Data.List  (intercalate)

newtype 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)

-- | Split a list into sublists of length n
-- group 2 [1..5] == [[1,2],[3,4],[5]]
group _ [] = []
group n xs = take n xs : group n (drop n xs)

-- | Create a matrix of indeces of a matrix
indeces :: Mat a -> Mat Pos
indeces (Mat m) = Mat (group y pos) where
	(x, y) = (length m, length (m !! 0))
	pos = liftA2 (,) [0..x-1] [0..y-1]

-- | Create a constant matrix
constant :: a -> Int -> Int -> Mat a
constant k x y = Mat (replicate x $ replicate y k)