1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
|
-- requires cabal install --lib megaparsec parser-combinators heap vector
module Main (main) where
import Control.Monad (void, when)
import Data.Functor
import qualified Data.Heap as H
import qualified Data.List as L
import qualified Data.Map as M
import qualified Data.Set as S
import qualified Data.Vector as V
import Data.Void (Void)
import Text.Megaparsec
import Text.Megaparsec.Char
exampleExpectedOutput = 64
data Tile = Wall | Floor | Start | End deriving (Eq, Show)
type Line = V.Vector Tile
type Input = V.Vector Line
type Parser = Parsec Void String
parseTile :: Parser Tile
parseTile = char '#' $> Wall
<|> char '.' $> Floor
<|> char 'E' $> End
<|> char 'S' $> Start
parseLine :: Parser Line
parseLine = do
line <- some parseTile <* eol
return $ V.generate (length line) (line !!)
parseInput' :: Parser Input
parseInput' = do
line <- some parseLine <* eof
return $ V.generate (length line) (line !!)
parseInput :: String -> IO Input
parseInput filename = do
input <- readFile filename
case runParser parseInput' filename input of
Left bundle -> error $ errorBundlePretty bundle
Right input' -> return input'
type Cost = Int
data Heading = N | S | E | W deriving (Eq, Ord, Show)
type Coord = (Int, Int, Heading)
type Path = S.Set Coord
data Position = Position Coord Cost Path deriving (Eq, Show)
instance Ord Position where
compare (Position _ c1 _) (Position _ c2 _) = c1 `compare` c2
type Visited = M.Map Coord Int
type Candidates = H.MinHeap Position
compute :: Input -> Int
compute input = S.size $ S.map (\(x, y, _) -> (x, y)) $ walk infinity M.empty $ H.singleton (Position start 0 S.empty)
where
walk :: Int -> Visited -> Candidates -> S.Set Coord
walk l v h | H.size h == 0 = S.empty
| c > l = walk l v' h'
| t == End = S.union s' $ walk c v' h'
| otherwise = walk l v' $ H.union h' $ H.fromList $ nexts v' $ Position p c s'
where
([(Position p@(x, y, d) c s)], h') = H.splitAt 1 h
t = input V.! y V.! x
v' = case M.lookup p v of
Just c' -> if c < c' then M.insert p c v else v
Nothing -> M.insert p c v
s' = S.insert p s
nexts :: Visited -> Position -> [Position]
nexts v p = L.filter (valid v) $ candidates p
valid :: Visited -> Position -> Bool
valid v (Position p@(x, y, _) c _) = input V.! y V.! x /= Wall && case M.lookup p v of
Just c' -> c <= c'
Nothing -> True
candidates :: Position -> [Position]
candidates (Position (x, y, N) c s) = [ Position (x-1, y, W) (c+1001) s, Position (x+1, y, E) (c+1001) s, Position (x, y-1, N) (c+1) s ]
candidates (Position (x, y, S) c s) = [ Position (x-1, y, W) (c+1001) s, Position (x+1, y, E) (c+1001) s, Position (x, y+1, S) (c+1) s ]
candidates (Position (x, y, E) c s) = [ Position (x, y-1, N) (c+1001) s, Position (x, y+1, S) (c+1001) s, Position (x+1, y, E) (c+1) s ]
candidates (Position (x, y, W) c s) = [ Position (x, y-1, N) (c+1001) s, Position (x, y+1, S) (c+1001) s, Position (x-1, y, W) (c+1) s ]
height = V.length input
width = V.length (input V.! 0)
start = (1, height - 2, E)
infinity = maxBound :: Int
main :: IO ()
main = do
example <- parseInput "example"
let exampleOutput = compute example
when (exampleOutput /= exampleExpectedOutput) (error $ "example failed: got " ++ show exampleOutput ++ " instead of " ++ show exampleExpectedOutput)
input <- parseInput "input"
print $ compute input
|
