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module Main where
import qualified Data.Set as Set
import Control.Monad
import Data.List
---
---
---
data Direction = DirUp | DirLeft | DirRight | DirDown
deriving (Eq,Ord,Show,Read)
directions = [DirUp,DirLeft,DirRight,DirDown]
coordOffset DirUp = (-1,0)
coordOffset DirLeft = (0,-1)
coordOffset DirRight = (0,1)
coordOffset DirDown = (1,0)
move (r,c) d = (r+dr,c+dc) where (dr,dc) = coordOffset d
sortPair (x,y) =
case compare x y of
EQ -> (x,y)
LT -> (x,y)
GT -> (y,x)
mapPair12 f (x,y) = (f x,f y)
cachedUsingList f = f'
where
list = map f [0..]
f' i = list !! i
nubSorted [] = []
nubSorted (x:xs) = nubSorted' x xs
where
nubSorted' x [] = [x]
nubSorted' x (y:ys)
| x == y = nubSorted' x ys
| otherwise = x : nubSorted' y ys
---
---
---
size = 21
largestExplicitlyEnumeratedArea = 7
type Cell = (Int,Int)
type Edge = (Cell,Cell)
mkEdge cell1 cell2 = sortPair (cell1,cell2)
cellsAround area = nubSorted $ sort $
do
cell <- area
dir <- directions
let cell2 = move cell dir
guard $ cell2 `notElem` area
return $ cell2
increaseAreas areas = nubSorted $ sort $
do
area <- areas
cell2 <- cellsAround area
return $ sort $ cell2 : area
getAreas :: Int -> [[Cell]]
getAreasRaw 1 = [[(0,0)]]
getAreasRaw n = areas
where
areas = increaseAreas $ getAreas $ n - 1
getAreas = cachedUsingList getAreasRaw
getEdges area = mapPair12 (map snd) $ partition fst $ nubSorted $ sort $
do
cell <- area
dir <- directions
let cell2 = move cell dir
let isInternal = cell2 `elem` area
return (isInternal,mkEdge cell cell2)
type SizedArea = (Int,((Set.Set Cell,Set.Set Cell),(Set.Set Edge,Set.Set Edge)))
getExtendedAreas n =
do
area <- getAreas n
let areaAround = cellsAround area
let edgeInfo = getEdges area
return ((Set.fromList area,Set.fromList areaAround),mapPair12 Set.fromList edgeInfo)
getSizedAreasThrough :: Int -> [SizedArea]
getSizedAreasThrough n =
do
n' <- [1 .. n]
extendedArea <- getExtendedAreas n'
return $ (n',extendedArea)
sizeForSizedArea (asize,_) = asize
allSizedAreas = getSizedAreasThrough largestExplicitlyEnumeratedArea
main = print $ allSizedAreas
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