[Haskell-cafe] xkcd #287 "NP-Complete"

[Donald Bruce Stewart]

trebla:
> http://xkcd.com/c287.html
> 
> import Data.Array
> import Control.Monad
> 
> -- exactly n v
> -- items in v that sum to exactly n
> -- returns list of solutions, each solution list of items
> exactly :: (Real a) => a -> Array Int a -> [[a]]
> exactly 0 v = return []
> exactly n v = do
>   i <- indices v
>   guard (v!i <= n)
>   liftM (v!i :) (exactly (n - v!i) (v `without` i))
> -- for solutions that use items multiple times,
> -- change (v `without` i) to v
> 
> -- v `without` i
> -- new array like v except one shorter with v!i missing
> without :: Array Int a -> Int -> Array Int a
> without v i = ixmap (lo, hi-1) f v
>     where (lo, hi) = bounds v
>           f j | j >= i = j+1
>               | otherwise = j
> 
> play = exactly 1505 menu
> menu = listArray (1,6) [215, 275, 335, 355, 420, 580]
> 
> test = exactly 10 (listArray (1,5) [1,1,2,3,4])
> 
> It disappoints me that there is no solution if each item is used at most 
> once. However, do change the code to allow multiple uses, then there are 
> many solutions.

These smaller NP problems really love the list monad. here's roconnor's
solution from #haskell:

    import Control.Monad

    menu = [("Mixed Fruit",215),("French Fries",275)
           ,("Side Salad",335),("Hot Wings",355)
           ,("Mozzarella Sticks",420),("Sampler Plate",580)]

    main = mapM_ print 
            [ map fst y 
            | i <- [0..]
            , y <- replicateM i menu
            , sum (map snd y) == 1505 ]

-- Don