module Data.Graph.AStar (aStar) where import qualified Data.Set as Set import Data.Set (Set, (\\)) import qualified Data.Map as Map import Data.Map (Map, (!)) import qualified Data.PSQueue as PSQ import Data.PSQueue (PSQ, Binding(..), minView) import Data.List (foldl') import Control.Monad (foldM) data AStar a c = AStar { visited :: !(Set a), waiting :: !(PSQ a c), score :: !(Map a c), memoHeur :: !(Map a c), cameFrom :: !(Map a a), end :: !(Maybe a) } deriving Show aStarInit start = AStar { visited = Set.empty, waiting = PSQ.singleton start 0, score = Map.singleton start 0, memoHeur = Map.empty, cameFrom = Map.empty, end = Nothing } runAStar :: (Ord a, Ord c, Num c) => (a -> Set a) -- adjacencies in graph -> (a -> a -> c) -- distance function -> (a -> c) -- heuristic distance to goal -> (a -> Bool) -- goal -> a -- starting vertex -> AStar a c -- final state runAStar graph dist heur goal start = aStar' (aStarInit start) where aStar' s = case minView (waiting s) of Nothing -> s Just (x :-> _, w') -> if goal x then s { end = Just x } else aStar' $ foldl' (expand x) (s { waiting = w', visited = Set.insert x (visited s)}) (Set.toList (graph x \\ visited s)) expand x s y = let v = score s ! x + dist x y in case PSQ.lookup y (waiting s) of Nothing -> link x y v (s { memoHeur = Map.insert y (heur y) (memoHeur s) }) Just _ -> if v < score s ! y then link x y v s else s link x y v s = s { cameFrom = Map.insert y x (cameFrom s), score = Map.insert y v (score s), waiting = PSQ.insert y (v + memoHeur s ! y) (waiting s) } -- | This function computes an optimal (minimal distance) path through a graph in a best-first fashion, -- starting from a given starting point. aStar :: (Ord a, Ord c, Num c) => (a -> Set a) -- ^ The graph we are searching through, given as a function from vertices -- to their neighbours. -> (a -> a -> c) -- ^ Distance function between neighbouring vertices of the graph. This will -- never be applied to vertices that are not neighbours, so may be undefined -- on pairs that are not neighbours in the graph. -> (a -> c) -- ^ Heuristic distance to the (nearest) goal. This should never overestimate the -- distance, or else the path found may not be minimal. -> (a -> Bool) -- ^ The goal, specified as a boolean predicate on vertices. -> a -- ^ The vertex to start searching from. -> Maybe [a] -- ^ An optimal path, if any path exists. This excludes the starting vertex. aStar graph dist heur goal start = let s = runAStar graph dist heur goal start in case end s of Nothing -> Nothing Just e -> Just (reverse . takeWhile (not . (== start)) . iterate (cameFrom s !) $ e) runAStarM :: (Monad m, Ord a, Ord c, Num c) => (a -> m (Set a)) -- adjacencies in graph -> (a -> a -> m c) -- distance function -> (a -> m c) -- heuristic distance to goal -> (a -> m Bool) -- goal -> a -- starting vertex -> m (AStar a c) -- final state runAStarM graph dist heur goal start = aStar' (aStarInit start) where aStar' s = case minView (waiting s) of Nothing -> return s Just (x :-> _, w') -> do g <- goal x if g then return (s { end = Just x }) else do ns <- graph x u <- foldM (expand x) (s { waiting = w', visited = Set.insert x (visited s)}) (Set.toList (ns \\ visited s)) aStar' u expand x s y = do d <- dist x y let v = score s ! x + d case PSQ.lookup y (waiting s) of Nothing -> do h <- heur y return (link x y v (s { memoHeur = Map.insert y h (memoHeur s) })) Just _ -> return $ if v < score s ! y then link x y v s else s link x y v s = s { cameFrom = Map.insert y x (cameFrom s), score = Map.insert y v (score s), waiting = PSQ.insert y (v + memoHeur s ! y) (waiting s) } -- | This function computes an optimal (minimal distance) path through a graph in a best-first fashion, -- starting from a given starting point. aStarM :: (Monad m, Ord a, Ord c, Num c) => (a -> m (Set a)) -- ^ The graph we are searching through, given as a function from vertices -- to their neighbours. -> (a -> a -> m c) -- ^ Distance function between neighbouring vertices of the graph. This will -- never be applied to vertices that are not neighbours, so may be undefined -- on pairs that are not neighbours in the graph. -> (a -> m c) -- ^ Heuristic distance to the (nearest) goal. This should never overestimate the -- distance, or else the path found may not be minimal. -> (a -> m Bool) -- ^ The goal, specified as a boolean predicate on vertices. -> m a -- ^ The vertex to start searching from. -> m (Maybe [a]) -- ^ An optimal path, if any path exists. This excludes the starting vertex. aStarM graph dist heur goal start = do sv <- start s <- runAStarM graph dist heur goal sv return $ case end s of Nothing -> Nothing Just e -> Just (reverse . takeWhile (not . (== sv)) . iterate (cameFrom s !) $ e) plane :: (Integer, Integer) -> Set (Integer, Integer) plane (x,y) = Set.fromList [(x-1,y),(x+1,y),(x,y-1),(x,y+1)] planeHole :: (Integer, Integer) -> Set (Integer, Integer) planeHole (x,y) = Set.filter (\(u,v) -> planeDist (u,v) (0,0) > 10) (plane (x,y)) planeDist :: (Integer, Integer) -> (Integer, Integer) -> Double planeDist (x1,y1) (x2,y2) = sqrt ((x1'-x2')^2 + (y1'-y2')^2) where [x1',y1',x2',y2'] = map fromInteger [x1,y1,x2,y2]