module Util.Grid where

type Position = (Int, Int)
type Direction = (Int, Int)

addpos :: Position -> Position -> Position
(x1, y1) `addpos` (x2, y2) = (x1 + x2, y1 + y2)

subpos :: Position -> Position -> Position
(x1, y1) `subpos` (x2, y2) = (x1 - x2, y1 - y2)

neighbours :: Position -> [Position]
neighbours (x, y) = [ (x-1,y-1), (x,y-1), (x+1,y-1),
                      (x-1,y), (x+1,y),
                      (x-1,y+1), (x,y+1), (x+1,y+1) ]

neighbours_and_self :: Position -> [Position]
neighbours_and_self pos = pos : neighbours pos

-- next_steps are the neighbours that are not directly reachable from
-- the parent.
next_steps :: Position -> Position -> [Position]
next_steps parent pos@(x, y) =
  case pos `subpos` parent of
    (0, 1)   -> [ (x,y+1), (x-1,y+1), (x+1,y+1) ]
    (0, -1)  -> [ (x,y-1), (x-1,y-1), (x+1,y-1) ]
    (1, 0)   -> [ (x+1,y), (x+1,y-1), (x+1,y+1) ]
    (-1, 0)  -> [ (x-1,y), (x-1,y-1), (x-1,y+1) ]
    (1, 1)   -> [ (x+1,y+1), (x,y+1), (x+1,y), (x-1,y+1), (x+1,y-1) ]
    (1, -1)  -> [ (x+1,y-1), (x,y-1), (x+1,y), (x-1,y-1), (x+1,y+1) ]
    (-1, 1)  -> [ (x-1,y+1), (x,y+1), (x-1,y), (x+1,y+1), (x-1,y-1) ]
    (-1, -1) -> [ (x-1,y-1), (x,y-1), (x-1,y), (x+1,y-1), (x-1,y+1) ]
    _ -> [ (x,y+1), (x+1,y), (x,y-1), (x-1,y),
           (x+1,y+1), (x+1,y-1), (x-1,y+1), (x-1,y-1) ]

posdist :: Position -> Position -> Int
(x1, y1) `posdist` (x2, y2) = max (abs (x1 - x2)) (abs (y1 - y2))

is_neighbour :: Position -> Position -> Bool
is_neighbour p1 p2 = (p1 `posdist` p2) <= 1