Hello again Ryan,
I have found out where to import those stuff from and tested your more elegant suggestion and my original performance.
-- print ((length ∘ pmsO [0,1]) 24) 9~ seconds
-- print ((length ∘ pmsE [0,1]) 24) 23~ seconds
-- print ((length ∘ pmsU [0,1]) 24) 23~ seconds
-- O: original, E: elegant, U: unreadable
I prefer performance over elegance (and for me using monads almost feels like adding an unnecessary dependency to the definition of pms. Though I know I may be dead wrong on that. I just don't quite understand monads yet.)
I would love to have you and/or others suggest more performant versions of pms (and maybe also come up with a better name for it).
mnt :: [a] → [[a]] → [[a]]
mnt [] _ = []
mnt _ [] = []
mnt (x:xs) yss = map (x:) yss ++ mnt xs yss
pms :: [a] → Int → [[a]]
pms [] _ = [[]]
pms _ 0 = [[]]
pms xxs n = mnt xxs (pms xxs (n - 1))
I generalized 'pms' from the 'bools' function on page 108 of Programming in Haskell (Hutton, 2007)
-- Cetin Sert
On 26/01/2008, Ryan Ingram <ryani.spam@gmail.com> wrote:
When you say permuations, I think of reorderings of a list, for example:
permutations [1,2,3] =
[ [1,2,3],
[1,3,2],
[2,1,3],
[2,3,1],
[3,1,2],
[3,2,1] ]
Here's an implementation:
-- split [1,2,3] => [
-- ( 1, [2,3] ),
-- ( 2, [1,3] ),
-- ( 3, [1,2] ) ]
split :: [a] -> [(a, [a])]
split [] = error "split: empty list"
split [a] = [(a, [])]
split (a:as) = (a, as) : map prefix (split as)
where prefix (x, xs) = (x, a : xs)
permutations :: [a] -> [[a]]
permutations [] = return []
permutations xs = do
(first, rest) <- split xs
rest' <- permutations rest
return (first : rest')
The problem you solved can be solved much more elegantly:
pms : [a] -> Int -> [[a]]
pms xs n = foldM combine [] (replicate n xs) where
combine rest as = liftM (:rest) as
or, for the unreadable version:
pms xs n = foldM (map . flip (:)) [] $ replicate n xs
(note that, in the list monad, liftM = map).
-- ryan