# [Haskell-cafe] lazy A-star search

Richard Senington sc06r2s at leeds.ac.uk
Sat Oct 22 17:35:45 CEST 2011

```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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