module Day9

import Prelude
import Node
import Aoc

parsePoint : String → Maybe Point
parsePoint text = case split text "," of
  a :: b :: Nil => Just (stringToInt a, stringToInt b)
  _ => Nothing

parse : String → List Point
parse text = mapMaybe parsePoint $ split (trim text) "\n"

abs : Int → Int
abs x = if x < 0 then 0 - x else x

data Line : U where
  VL : (x y1 y2 : Int) → Line
  HL : (y x1 x2 : Int) → Line

instance Show Line where
  show (VL x y1 y2) = "VL \{show (x,y1,y2)}"
  show (HL x y1 y2) = "HL \{show (x,y1,y2)}"

data Box = B Int Int Int Int

instance Show Box where
  show (B l r t b) = "Box \{show (l,r,t,b)}"

area : Box → Int
area (B l r t b) = (abs (l - r) + 1) * (abs (t - b) + 1)

mkbox : Point → Point → Box
mkbox (a,b) (c,d) = B (min a c) (max a c) (min b d) (max b d)

boxes : List Point → List Box
boxes pts = go pts Nil
  where
    go2 : Point → List Point → List Box → List Box
    go2 pt (x :: xs) acc = go2 pt xs (mkbox pt x :: acc)
    go2 pt _ acc = acc

    go : List Point → List Box → List Box
    go (pt :: rest) acc = go rest $ go2 pt rest acc
    go Nil acc = acc

-- line intersects middle of a box
isect : Box → Line → Bool
isect (B l r t b) (VL x y1 y2) = x < r && l < x && y1 < b && t < y2
isect (B l r t b) (HL y x1 x2) = y < b && t < y && x1 < r && l < x2

getLines : List Point → List Line
getLines points = go points Nil
  where
    go : List Point → List Line → List Line
    go ((a,b) :: rest@((c,d) :: _)) acc =
      if a == c
        then let seg = if b < d then VL a b d else VL a d b in go rest (seg :: acc)
        else if b == d then let seg = if a < c then HL b a c else HL b c a in go rest (seg :: acc)
        else Nil
    go _ acc = acc

-- I'm assuming the winner isn't a single row/column
part2 : List (Int × Box) → List Line → Int
part2 Nil _ = 0
part2 ((size, box) :: rest) lines = if checkRec box then size else part2 rest lines
  where
    winds : Box → Line → Bool
    winds (B l r t b) (VL x y1 y2) =
      -- pick a point in the middle, the rest is connected because no intersection
      if t == b then False else r <= x && y1 < t + 1 && t + 1 < y2
    winds (B l r t b) (HL x y1 y2) = False

    checkRec : Box → Bool
    checkRec box =
      let (Nothing) = find (isect box) lines | _ => False in
      let winding = length' $ filter (winds box) lines in mod winding 2 == 1

run : String -> IO Unit
run fn = do
  putStrLn fn
  text <- readFile fn
  let (pts@(a :: _)) = parse text | _ => putStrLn "empty input"
  -- printLn pts
  let sortBoxes = qsort (\ a b => fst a > fst b) $ map (\box => (area box, box)) $ boxes pts
  let ((p1,_) :: _ ) = sortBoxes | _ => printLn "no boxes"
  putStrLn $ "part1 \{show p1}"
  let vl = getLines $ a :: reverse pts
  putStrLn $ "part2 " ++ show (part2 sortBoxes vl)

main : IO Unit
main = do
  run "aoc2025/day9/eg.txt"
  run "aoc2025/day9/input.txt"