[Haskell-cafe] Re: breadth first search one-liner?
apfelmus at quantentunnel.de
Thu Mar 25 04:36:09 EDT 2010
Johannes Waldmann wrote:
> Dear all, there is this neat "one-line" BFS implementation
> bfs :: Eq a
> => ( a -> [a] ) -> a -> [a]
> bfs next start =
> let xs = nub $ start : ( xs >>= next )
> in xs
> but it has a problem: it only works for infinite graphs. This is fine:
> take 20 $ bfs ( \ x -> [2*x, x+1] ) 1
> but this is not:
> take 20 $ bfs ( \ x -> filter (>0) [ div x 2, x - 1 ] ) 10
> Is there a nice way to repair this?
> (I know how to code a BFS but here I'm asking for a one-liner.)
There is a neat trick to handle the finite case which I first read about
in Leon P. Smith's article
Lloyd Allison’s Corecursive Queues: Why Continuations Matter.
Namely, you have to keep track of the "current" queue size so that the
program doesn't hang when the queue becomes empty:
bfs' f x = let xs = more 1 (x:xs) in x:xs
more 0 _ = 
more n (x:xs) = f x ++ more (n + length (f x) - 1) xs
Unfortunately, this cannot be made to work with nub because that would
screw up the size calculation.
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