module Satchmo.Counting.Direct
( atleast
, atmost
, exactly
)
where
import Satchmo.Boolean ( Boolean, MonadSAT )
import qualified Satchmo.Boolean as B
import Control.Monad ( forM )
select :: Int -> [a] -> [[a]]
select 0 xs = [[]]
select k [] = []
select k (x:xs) =
select k xs ++ (map (x:) $ select (k1) xs)
atleast :: MonadSAT m => Int -> [ Boolean ] -> m Boolean
atleast k xs = B.or =<< forM (select k xs) B.and
atmost :: MonadSAT m => Int -> [ Boolean ] -> m Boolean
atmost k xs = atleast (length xs k) $ map B.not xs
exactly :: MonadSAT m => Int -> [ Boolean ] -> m Boolean
exactly k xs = do
this <- atleast k xs
that <- atmost k xs
this B.&& that