I mean "can be used in practice, no only for toy examples"

2011/10/22 Richard Senington <sc06r2s@leeds.ac.uk>

How do you mean effective?

While I am not sure they mention A* search, you might like to look at the paper
"Modular Lazy Search for Constraint Satisfaction Problems" by Nordin & Tolmach.
http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.4704

RS

On 22/10/11 13:28, Anton Kholomiov wrote:
Recently I was looking for an A-star search algorithm. I've found a package
but I couldn't understand the code. Then I saw some blogposts but they

were difficult to understand too. I thought about some easier solution that

relies on laziness. And I've come to this:

Heuristic search is like depth-first search but solutions in sub-trees

are concatenated with mergeBy function, that concatenates two

list by specific order:

module Search where

import Control.Applicative

import Data.Function(on)

import Control.Arrow(second)

import Data.Tree

-- | Heuristic search. Nodes are visited from smaller to greater.

searchBy :: (a -> a -> Ordering) -> Tree a -> [a]

searchBy heur (Node v ts) =

   v : foldr (mergeBy heur) [] (searchBy heur <$> ts)

-- | Merge two lists. Elements concatenated in specified order.

mergeBy :: (a -> a -> Ordering) -> [a] -> [a] -> [a]

mergeBy _ a [] = a

mergeBy _ [] b = b

mergeBy p (a:as) (b:bs)

   | a `p` b == LT = a : mergeBy p as (b:bs)

   | otherwise = b : mergeBy p bs (a:as)

Now we can define specific heuristic search in terms of searchBy:

-- | Heuristic is distance to goal.

bestFirst :: Ord h => (a -> h) -> (a -> [a]) -> a -> [a]

bestFirst dist alts =

   searchBy (compare `on` dist) . unfoldTree (\a -> (a, alts a))

-- | A-star search.

-- Heuristic is estimated length of whole path.

astar :: (Ord h, Num h) => (a -> h) -> (a -> [(a, h)]) -> a -> [a]

astar dist alts s0 = fmap fst $

   searchBy (compare `on` astarDist) $ unfoldTree gen (s0, 0)

   where astarDist (a, d) = dist a + d

   gen (a, d) = d `seq` ((a, d), second (+d) <$> alts a)

I'm wondering is it effective enough?

Anton
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