-- IB016 Seminar on Functional Programming
-- Task from lecture 01

import qualified Data.Map.Strict as M

newtype Point = P { unP :: (Double, Double) } deriving (Eq, Ord, Show)

type Canvas = M.Map Point Char

exampleCanvas1 :: Canvas
exampleCanvas1 = M.fromList 
  [ (P (0,0), 'A')
  , (P (1,1), 'B')
  , (P (2,2), 'C')
  , (P (3,1), 'D')
  , (P (4,0), 'E')
  , (P (5,7), 'F')
  , (P (-2,-1), 'G')
  ]

furthestFrom :: Point -> Canvas -> Maybe Char
furthestFrom origin canvas = snd <$> (M.lookupMax $ M.mapKeys (distance origin) canvas)
  where distance (P (x1, y1)) (P (x2, y2)) = sqrt $ (x2-x1)^(2::Int) + (y2-y1)^(2::Int)

linePoints :: Point -> Point -> Canvas -> [Char]
linePoints (P (x1, y1)) (P (x2, y2)) canvas = M.elems $ M.filterWithKey onLine canvas
  where onLine (P (x, y)) _  = y - y1 == slope * (x - x1)
        slope = (y2 - y1) / (x2 - x1)

reflectY :: Canvas -> Canvas
reflectY canvas = M.union canvas $ M.mapKeys reflect canvas
  where reflect (P (x,y)) = P (-x, y)