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71 lines
2.9 KiB
Haskell
71 lines
2.9 KiB
Haskell
{ Copyright 2012 Abhinav Sarkar <abhinav@abhinavsarkar.net> }




{# LANGUAGE MultiParamTypeClasses #}




module AStar (astar) where




import qualified Data.PQueue.Prio.Min as PQ


import qualified Data.Set as S


import qualified Data.Map as M


import Data.List (foldl')


import Data.Maybe (fromJust)




  A* algorithm: Finds a path from initial node to goal node using a heuristic function.


astar :: (Ord a, Ord b, Num b) =>


a  ^ The start node


> a  ^ The goal node


> (a > [(a, b)])  ^ The function to get the next nodes and their


 costs from a given node


> (a > a > b)  ^ The heuristic function to estimate the cost of


 going from a give node to the target node


> Maybe (b, [a])  ^ Nothing if no path found. Else @Just (path cost, path)@


astar initNode goalNode nextNode hueristic =


astar' (PQ.singleton (hueristic initNode goalNode) (initNode, 0))


S.empty (M.singleton initNode 0) M.empty


where


 pq: open set, seen: closed set, tracks: tracks of states


astar' pq seen gscore tracks


 If open set is empty then search has failed. Return Nothing


 PQ.null pq = Nothing


 If goal node reached then construct the path from the tracks and node


 node == goalNode = Just (gcost, findPath tracks node)


 If node has already been seen then discard it and continue


 S.member node seen = astar' pq' seen gscore tracks


 Else expand the node and continue


 otherwise = astar' pq'' seen' gscore' tracks'


where


 Find the node with min fcost


(node, gcost) = snd . PQ.findMin $ pq




 Delete the node from open set


pq' = PQ.deleteMin pq




 Add the node to the closed set


seen' = S.insert node seen




 Find the successors (with their g and h costs) of the node


 which have not been seen yet


successors =


filter (\(s, g, _) >


not (S.member s seen') &&


(not (s `M.member` gscore)


 g < (fromJust . M.lookup s $ gscore)))


$ successorsAndCosts node gcost




 Insert the successors in the open set


pq'' = foldl' (\q (s, g, h) > PQ.insert (g + h) (s, g) q) pq' successors




gscore' = foldl' (\m (s, g, _) > M.insert s g m) gscore successors




 Insert the tracks of the successors


tracks' = foldl' (\m (s, _, _) > M.insert s node m) tracks successors




 Finds the successors of a given node and their costs


successorsAndCosts node gcost =


map (\(s, g) > (s, gcost + g, hueristic s goalNode)) . nextNode $ node




 Constructs the path from the tracks and last node


findPath tracks node =


if M.member node tracks


then findPath tracks (fromJust . M.lookup node $ tracks) ++ [node]


else [node] 