115 lines
4.1 KiB
Haskell
115 lines
4.1 KiB
Haskell
module Main where
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import Control.Monad (forM_)
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import Data.List (intercalate)
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import Debug.Trace (trace)
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import Math.NumberTheory.Roots (integerSquareRoot, integerCubeRoot)
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type Cell = Int -- ^ The index of a cell in the cube
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type Peel = Int -- ^ A peel of our cube
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type Ring = Int -- ^ A ring of a 2D spiral
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type Length = Int -- ^ The length of an line segment
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type X = Int
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type Y = Int
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type Z = Int
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type Point2D = (X, Y)
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type Point3D = (X, Y, Z)
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area :: Int -> Int
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area a = a * a
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cube :: Int -> Int
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cube a = a * a * a
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ring :: Cell -> Ring
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ring o = integerSquareRoot o `div` 2
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peel :: Cell -> Peel
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peel c = integerCubeRoot c `div` 2
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edge :: Peel -> Length
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edge l = 2 * l + 2
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atZ :: Z -> Point2D -> Point3D
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atZ z (x, y) = (x, y, z)
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reflectY :: Point2D -> Point2D
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reflectY (x, y) = (x, -y - 1)
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reflectX :: Point2D -> Point2D
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reflectX (x, y) = (-x - 1, y)
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reflectX3 :: Point3D -> Point3D
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reflectX3 (x, y, z) = (-x - 1, y, z)
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reflectZ3 :: Point3D -> Point3D
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reflectZ3 (x, y, z) = (x, y, -z - 1)
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rotate :: Length -> Point2D -> Point2D
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rotate l (x, y) = (-y - 1, -x - 1)
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spirals :: Length -> Cell -> Point3D
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spirals l c = atZ h $ case h `mod` 4 of
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0 -> growingSpiral l o
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1 -> rotate l $ shrinkingSpiral l o
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2 -> reflectX . reflectY $ growingSpiral l o
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3 -> reflectX . reflectY . rotate l $ shrinkingSpiral l o
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where h = c `div` area l
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o = c - h * area l
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z = h - l `div` 2 - 1
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growingSpiral :: Length -> Cell -> Point2D
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growingSpiral l o | o == 0 = (0, 0)
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| ro < e - 1 = (r, ro - r) -- 64
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| ro < 2 * e - 2 = (3 * r - ro, r)
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| ro < 3 * e - 3 = (0 - r - 1, 5 * r - ro + 1)
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| otherwise = (ro - 7 * r - 3, 0 - r - 1)
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where r = ring o -- ^ the current spiral ring
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ro = o - area (edge $ r - 1) -- ^ offset within this ring
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e = edge r -- ^ edge of the this ring
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shrinkingSpiral :: Length -> Cell -> Point2D
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shrinkingSpiral l o = growingSpiral l (area l - o - 1)
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peeledCubes :: Length -> Cell -> Point3D
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peeledCubes _ c | o < a = reverseIfOdd
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. atZ (e `div` 2 - 1) -- on top of the cube
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$ growingSpiral e o
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| o < a + (e - 2) * (e - 1) * 4
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= reverseIfOdd
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$ mantel p e (o - a)
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| otherwise
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= reverseIfOdd
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. atZ (-e `div` 2) -- on the bottom of the cube
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. reflectX
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$ shrinkingSpiral e (o - a - (e - 2) * (e - 1) * 4)
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where p = peel c -- ^ the current peel
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o = c - cube (edge $ p - 1) -- ^ offset within the current peel
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e = edge p -- ^ the length of the edge of the current peel
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a = area e -- ^ the area of a side of the current peel
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reverseIfOdd = if p `mod` 2 == 0 then id else (reflectX3 . reflectZ3)
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mantel :: Peel -> Length -> Cell -> Point3D
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mantel p e m | o <= r = (p - r + o, 0 - p - 1, p - r - 1)
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| o <= r + e - 1 = (p, 0 - p - 1 + o - r, p - r - 1)
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| o <= r + 2 * e - 2 = (p - o + r + e - 1, p, p - r - 1)
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| o <= r + 3 * e - 3 = (0 - p - 1, p - o + r + 2 * e - 2, p - r - 1)
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| otherwise = (0 - p - 1 + o - r - 3 * e + 3, 0 - p - 1, p - r - 1)
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where r = m `div` (4 * e - 4) -- ^ revolutions since starting on the side
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o = m - (4 * e - 4) * r -- ^ offset within this revolution
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asMatrix :: Length -> [[[Cell]]]
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asMatrix e = foldl (\c (i, x, y, z) -> replace c z $ replace (c!!z) y $ replace (c!!z!!y) x i)
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(replicate e $ replicate e $ replicate e (-1))
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[ (i, x + div e 2, y + div e 2, z + div e 2)
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| i <- [0..cube e - 1]
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, let (x, y, z) = peeledCubes e i
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]
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where replace :: [a] -> Int -> a -> [a]
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replace l i e = take i l ++ [e] ++ drop (i+1) l
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main :: IO ()
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main = forM_ (reverse $ asMatrix 6) $ \plane -> do
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forM_ (reverse plane) $ \row -> do
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putStrLn $ intercalate ",\t" $ map show row
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putStrLn ""
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