172 lines
6.6 KiB
Haskell
172 lines
6.6 KiB
Haskell
{-# LANGUAGE Strict #-}
|
|
module Main where
|
|
|
|
import Control.Applicative (some)
|
|
import Data.Bits (Bits(shift))
|
|
import Data.Function (on)
|
|
import qualified Data.Set as Set
|
|
import qualified Data.Tree as T
|
|
import Data.List (maximumBy, foldl', sort)
|
|
import Data.Ord (comparing)
|
|
import Text.Parsec hiding (Empty)
|
|
|
|
data Rect = Rect { rectID :: Int
|
|
, rectLeft :: Int
|
|
, rectTop :: Int
|
|
, rectWidth :: Int
|
|
, rectHeight :: Int
|
|
}
|
|
|
|
instance Eq Rect where
|
|
(==) = (==) `on` rectID
|
|
|
|
instance Ord Rect where
|
|
compare = compare `on` rectID
|
|
|
|
instance Show Rect where
|
|
show (Rect id l t w h) = "#" ++ show id ++ " " ++ show l ++ "," ++ show t ++ ":" ++ show (l+w) ++ "," ++ show (t+h)
|
|
|
|
inputP :: Parsec String () Rect
|
|
inputP =
|
|
(\id (l,t) (w,h) -> Rect id l t w h)
|
|
<$> (idP <* spaces <* char '@' <* spaces)
|
|
<*> (posP <* char ':' <* spaces)
|
|
<*> dimP
|
|
where
|
|
intP = read <$> some digit
|
|
idP = char '#' *> intP
|
|
posP = (,) <$> (intP <* char ',') <*> intP
|
|
dimP = (,) <$> (intP <* char 'x') <*> intP
|
|
|
|
readInput :: [String] -> [Rect]
|
|
readInput ls = case traverse (parse inputP "") ls of
|
|
Left e -> error (show e)
|
|
Right rs -> rs
|
|
|
|
sheetSize :: [Rect] -> (Int, Int)
|
|
sheetSize rects =
|
|
( calcBound (\(Rect _ l _ w _) -> l + w)
|
|
, calcBound (\(Rect _ _ t _ h) -> t + h))
|
|
where
|
|
calcBound f = f (maximumBy (comparing f) rects)
|
|
|
|
isOverlapCell :: [Rect] -> (Int, Int) -> Bool
|
|
isOverlapCell rects cell =
|
|
(> 1) . length . take 2 . filter (cellInRect cell) $ rects
|
|
where
|
|
cellInRect (x, y) (Rect _ l t w h) =
|
|
l <= x && (l+w) >= (x+1) && t <= y && (t+h) >= (y+1)
|
|
|
|
---------------- Brute force ----------------
|
|
|
|
bruteForceSolve :: [Rect] -> (Int, [Rect])
|
|
bruteForceSolve rects =
|
|
let (w, h) = sheetSize rects
|
|
cells = [(i, j) | i <- [0..w-1], j <- [0..h-1]]
|
|
overlapArea = length . filter (isOverlapCell rects) $ cells
|
|
noOverlapRects = filter (\r -> not $ any (\r1 -> r1 /= r && r1 `overlaps` r) rects) rects
|
|
in (overlapArea, noOverlapRects)
|
|
where
|
|
(Rect _ l1 t1 w1 h1) `overlaps` (Rect _ l2 t2 w2 h2) =
|
|
l1 < (l2+w2) && (l1+w1) > l2 && t1 < (t2+h2) && (t1+h1) > t2
|
|
|
|
---------------- Interval tree ----------------
|
|
|
|
newtype Interval a = Interval { unInterval :: (a,a) } deriving (Eq, Ord)
|
|
|
|
instance Show a => Show (Interval a) where
|
|
show (Interval (a, b)) = "<" ++ show a ++ "," ++ show b ++ ">"
|
|
|
|
data IntervalTree a b = Node { itLeft :: IntervalTree a b
|
|
, itCenter :: a
|
|
, itIntervals :: [(Interval a, b)]
|
|
, itRight :: IntervalTree a b
|
|
}
|
|
| Empty a a deriving (Show, Eq)
|
|
|
|
rightOf, leftOf :: Ord a => Interval a -> a -> Bool
|
|
rightOf (Interval (start, _)) x = x < start
|
|
leftOf (Interval (_, end)) x = end <= x
|
|
|
|
insert :: (Ord a, Ord b, Bits a, Num a) => (Interval a, b) -> IntervalTree a b -> IntervalTree a b
|
|
insert o@(interval, _) tree = case tree of
|
|
Empty start end -> go start end (start + half (end - start))
|
|
Node l center is r | interval `leftOf` center -> Node (insert o l) center is r
|
|
Node l center is r | interval `rightOf` center -> Node l center is (insert o r)
|
|
Node l center is r -> Node l center (sort (o:is)) r
|
|
where
|
|
go start end center
|
|
| interval `leftOf` center = Node (insert o (Empty start center)) center [] (Empty center end)
|
|
| interval `rightOf` center = Node (Empty start center) center [] (insert o (Empty center end))
|
|
| otherwise = Node (Empty start center) center [o] (Empty center end)
|
|
|
|
half = flip shift (-1)
|
|
|
|
overlappingIntervals :: Ord a =>
|
|
(Interval a -> Interval a -> Bool) -> Interval a -> IntervalTree a b -> [(Interval a, b)]
|
|
overlappingIntervals f interval = go []
|
|
where
|
|
go acc t = case t of
|
|
Empty _ _ -> acc
|
|
Node l _ is _ | not (null is) && interval `leftOf` leftmostStart is -> go acc l
|
|
Node l center is _ | interval `leftOf` center -> go (acc' is acc) l
|
|
Node _ center is r | interval `rightOf` center -> go (acc' is acc) r
|
|
Node l _ is r -> go (go (acc' is acc) l) r
|
|
where
|
|
acc' is acc = filter (\(i,_) -> i `f` interval) is ++ acc
|
|
leftmostStart = fst . unInterval . fst . head
|
|
|
|
includingIntervals :: Ord a => Interval a -> IntervalTree a b -> [(Interval a, b)]
|
|
includingIntervals =
|
|
overlappingIntervals $ \(Interval (start1, end1)) (Interval (start2, end2)) ->
|
|
start1 <= start2 && end2 <= end1
|
|
|
|
intersectingIntervals :: Ord a => Interval a -> IntervalTree a b -> [(Interval a, b)]
|
|
intersectingIntervals =
|
|
overlappingIntervals $ \(Interval (start1, end1)) (Interval (start2, end2)) ->
|
|
start2 < end1 && start1 < end2
|
|
|
|
fromList :: (Ord a, Ord b, Bits a, Num a) => a -> a -> [(Interval a, b)] -> IntervalTree a b
|
|
fromList start end = foldl' (flip insert) (Empty start end)
|
|
|
|
toInterval :: (Rect -> Int) -> (Rect -> Int) -> Rect -> Interval Int
|
|
toInterval pos dim rect = Interval (pos rect, pos rect + dim rect)
|
|
|
|
rectIntervalTrees :: [Rect] -> (IntervalTree Int Rect, IntervalTree Int Rect)
|
|
rectIntervalTrees rects =
|
|
let (w, h) = sheetSize rects
|
|
in ( fromList 0 w . map (\r -> (toInterval rectLeft rectWidth r, r)) $ rects
|
|
, fromList 0 h . map (\r -> (toInterval rectTop rectHeight r, r)) $ rects
|
|
)
|
|
|
|
toTree :: (Show a, Show b) => IntervalTree a b -> T.Tree String
|
|
toTree (Empty start end) = T.Node (show ("E", start, end)) []
|
|
toTree (Node l c is r) = T.Node (show ("N", c, is)) [toTree l, toTree r]
|
|
|
|
intervalTreeSolve :: [Rect] -> (Int, [Rect])
|
|
intervalTreeSolve rects =
|
|
let (w, h) = sheetSize rects
|
|
cells = [(i, j) | i <- [0..w-1], j <- [0..h-1]]
|
|
(xTree, yTree) = rectIntervalTrees rects
|
|
overlapArea = length . filter (\c -> isOverlapCell (cellRects xTree yTree c) c) $ cells
|
|
noOverlapRects = filter ((== 1) . Set.size . overlappingRects xTree yTree) rects
|
|
in (overlapArea, noOverlapRects)
|
|
where
|
|
cellRects xTree yTree (x,y) =
|
|
nub . map snd
|
|
$ includingIntervals (Interval (x, x+1)) xTree ++ includingIntervals (Interval (y, y+1)) yTree
|
|
|
|
nub = Set.toList . Set.fromList
|
|
|
|
rectIntervals tree pos dim rect =
|
|
Set.fromList . map snd . intersectingIntervals (toInterval pos dim rect) $ tree
|
|
|
|
overlappingRects xTree yTree rect =
|
|
rectIntervals xTree rectLeft rectWidth rect `Set.intersection` rectIntervals yTree rectTop rectHeight rect
|
|
|
|
main :: IO ()
|
|
main = do
|
|
rects <- readInput . lines <$> getContents
|
|
let (overlapArea, noOverlapRects) = bruteForceSolve rects
|
|
putStrLn $ "Overlap Area = " ++ show overlapArea
|
|
putStrLn $ "No overlap rects = " ++ show noOverlapRects |