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
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
|
-- requires cabal install --lib megaparsec parser-combinators heap vector
module Main (main) where
import Control.Applicative.Permutations
import Control.Monad (void, when)
import qualified Data.Char as C
import Data.Either
import Data.Functor
import qualified Data.Heap as H
import qualified Data.List as L
import qualified Data.Map as M
import Data.Maybe
import qualified Data.Set as S
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as VU
import Data.Void (Void)
import Text.Megaparsec
import Text.Megaparsec.Char
import Debug.Trace
exampleExpectedOutput = Just 94
data Direction = N | S | E | W deriving (Eq, Show)
data Tile = Floor | Wall | Slope Direction deriving (Eq, Show)
type Line = V.Vector Tile
type Input = V.Vector Line
type Parser = Parsec Void String
parseDirection :: Parser Direction
parseDirection = char '^' $> N
<|> char 'v' $> S
<|> char '>' $> E
<|> char '<' $> W
parseTile :: Parser Tile
parseTile = char '#' $> Wall
<|> char '.' $> Floor
<|> Slope <$> parseDirection
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'
newtype Cost = Cost Int deriving (Eq, Num, Ord, Show)
newtype NodeId = NodeId Int deriving (Eq, Num, Ord, Show)
newtype X = X Int deriving (Eq, Num, Ord, Show)
newtype Y = Y Int deriving (Eq, Num, Ord, Show)
type Adjacencies = M.Map NodeId [(NodeId, Cost)] -- keys are nodeIds and values are a list of (NodeId, cost)
type Nodes = M.Map (X, Y) NodeId -- keys are (x, y) and values are nodeIds
type Visited = M.Map (X, Y) ()
compute :: Input -> Maybe Cost
compute input = longuestPath adjacencies (let Just (a:[]) = M.lookup 0 adjacencies in a)
where
longuestPath :: Adjacencies -> (NodeId, Cost) -> Maybe Cost
longuestPath adj (n, c) | n == 1 = Just $ c + 1
| l' == [] = Nothing
| otherwise = Just $ c + maximum l'
where
Just l = M.lookup n adj
l' = catMaybes $ L.map (longuestPath adj') l
adj' = M.delete n $ M.map (L.filter (\(i, _) -> n /= i)) adj
(adjacencies, nodes, _) = explore 0 (M.fromList [(0, []), (1, [])]) (M.fromList [((startx, 0), 0), ((finishx, finishy), 1)]) (M.fromList [((startx, 0), ()), ((finishx, finishy), ())]) startx 1 S
explore :: NodeId -> Adjacencies -> Nodes -> Visited -> X -> Y -> Direction -> (Adjacencies, Nodes, Visited)
explore node adjacencies nodes visited x y d = L.foldl' explore' (adjacencies, nodes, visited) $ nextSteps x y d
where
explore' :: (Adjacencies, Nodes, Visited) -> (X, Y, Direction, Bool) -> (Adjacencies, Nodes, Visited)
explore' acc@(adjacencies, nodes, visited) (x, y, d, u) | isNothing destination = acc
| otherwise = case M.lookup (x', y') nodes of
Nothing -> explore node' adjacencies'' nodes' visited' x' y' d
Just id -> (adjacencies'', nodes', visited')
where
destination = let s = goDownAPath visited False x y 1 d in s
Just (visited', x', y', cost, u') = destination
adjacencies'' = M.adjust (\l -> (node', cost):l) node $ M.adjust (\l -> if u || u' then l else (node, cost):l) node' adjacencies'
nodes' = M.insert (x', y') node' nodes
(node', adjacencies') = case M.lookup (x', y') nodes of
Nothing -> let s = NodeId (M.size nodes) in (s, M.insert s [] adjacencies)
Just node' -> (node', adjacencies)
goDownAPath :: Visited -> Bool -> X -> Y -> Cost -> Direction -> Maybe (Visited, X, Y, Cost, Bool) -- returns the next intersection's coordinates and cost, and if it is unidirectional
goDownAPath visited u x y c d | M.member (x, y) nodes = Just (visited, x, y, c, u) -- we reached an already known intersection
| M.member (x, y) visited = Nothing -- this tile has already been visited
| isImpossibleSlope = Nothing
| ns == [] = Nothing -- we hit a deadend
| L.length ns > 1 = Just (visited', x, y, c, u'') -- we hit a crossroads
| otherwise = goDownAPath visited' u'' x' y' (c+1) d'
where
(x', y', d', u') = head ns
u'' = u || u'
ns = nextSteps x y d
visited' = M.insert (x, y) () visited
isImpossibleSlope = case getTile (x, y) of
Slope s -> s /= d
otherwise -> False
getTile :: (X, Y) -> Tile
getTile (X x, Y y) = input V.! y V.! x
nextSteps :: X -> Y -> Direction -> [(X, Y, Direction, Bool)] -- get the list of possible next steps at a point, given where we came from
nextSteps x y d = L.map augmentWithUnidirectionality $ L.filter possible [(x-1, y, W), (x+1, y, E), (x, y-1, N), (x, y+1, S)]
where
augmentWithUnidirectionality :: (X, Y, Direction) -> (X, Y, Direction, Bool)
augmentWithUnidirectionality (x, y, d) = (x, y, d, isSlope $ getTile (x, y))
isSlope :: Tile -> Bool
isSlope (Slope _) = True
isSlope _ = False
possible :: (X, Y, Direction) -> Bool
possible (x', y', d') | t == Wall = False
| d == opposite d' = False -- no going back
-- | t == Floor = True
| otherwise = True -- o == d' -- our direction must match the slope <- NO, this prevents us from properly finding intersections
where
t = getTile (x', y')
Slope o = t
Just start = V.findIndex (== Floor) $ input V.! 0
startx = X start
Just finish = V.findIndex (== Floor) $ input V.! finishyy
finishx = X finish
finishyy = V.length input - 1
finishy = Y finishyy
xydToxy :: (a, b, c) -> (a, b)
xydToxy (x, y, _) = (x, y)
opposite :: Direction -> Direction
opposite N = S
opposite S = N
opposite E = W
opposite W = E
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
|
