module Part2 where

import Commons
import Data.Array (assocs, bounds, (//))


getReachableOdd :: Garden -> Int
getReachableOdd garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      n = (yMax - yMin + div (yMax - yMin) 2)
      newGarden = garden // [((1 + div (yMax - yMin) 2, 1 + div (xMax - xMin) 2), Plot {reachable = True})]
  in length $ getReachableAfterNMove n newGarden

getReachableEven :: Garden -> Int
getReachableEven garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      n = (yMax - yMin + 1 + div (yMax - yMin) 2)
      newGarden = garden // [((1 + div (yMax - yMin) 2, 1 + div (xMax - xMin) 2), Plot {reachable = True})]
  in length $ getReachableAfterNMove n newGarden

getReachableCardinals :: Garden -> [Int]
getReachableCardinals garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      n = yMax - yMin
      (yMean, xMean) = (1 + div (yMax - yMin) 2, 1 + div (xMax - xMin) 2)
  in [length $ getReachableAfterNMove n $ garden // [((yMean, xMin), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMean, xMax), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMin, xMean), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMax, xMean), Plot {reachable = True})]]

getReachableOddCorners :: Garden -> [Int]
getReachableOddCorners garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      n = yMax - yMin + div (yMax - yMin) 2
  in [length $ getReachableAfterNMove n $ garden // [((yMin, xMin), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMin, xMax), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMax, xMin), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMax, xMax), Plot {reachable = True})]]

getReachableEvenCorners :: Garden -> [Int]
getReachableEvenCorners garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      n = div (yMax - yMin) 2 - 1
  in [length $ getReachableAfterNMove n $ garden // [((yMin, xMin), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMin, xMax), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMax, xMin), Plot {reachable = True})],
      length $ getReachableAfterNMove n $ garden // [((yMax, xMax), Plot {reachable = True})]]

getReachableAfterN :: Int -> Garden -> Int
getReachableAfterN n garden =
  let ((yMin, xMin), (yMax, xMax)) = bounds garden
      x = div (n - div (yMax - yMin) 2) (yMax - yMin + 1)
  in x * x * getReachableEven garden + x * sum (getReachableEvenCorners garden)
     + (x - 1) * (x - 1) * getReachableOdd garden + (x - 1) * sum (getReachableOddCorners garden)
     + sum (getReachableCardinals garden)