Am Dienstag 04 August 2009 19:48:25 schrieb Slavomir Kaslev: > A friend mine, new to functional programming, was entertaining himself by > writing different combinatorial algorithms in Haskell. He asked me for some > help so I sent him my quick and dirty solutions for generating variations > and > > permutations: > > inter x [] = [[x]] > > inter x yys@(y:ys) = [x:yys] ++ map (y:) (inter x ys) > > > > perm [] = [[]] > > perm (x:xs) = concatMap (inter x) (perm xs) > > > > vari 0 _ = [[]] > > vari _ [] = [] > > vari k (x:xs) = concatMap (inter x) (vari (k-1) xs) ++ vari k xs > > After that I found out that nowadays there is a permutation function in the > > Data.List module: > > permutations :: [a] -> [[a]] > > permutations xs0 = xs0 : perms xs0 [] > > where > > perms [] _ = [] > > perms (t:ts) is = foldr interleave (perms ts (t:is)) (permutations > > is) where interleave xs r = let (_,zs) = interleave' id xs r in zs > > interleave' _ [] r = (ts, r) > > interleave' f (y:ys) r = let (us,zs) = interleave' (f . (y:)) > > ys r in (y:us, f (t:y:us) : zs) > > I was surprised to find that not only my version is much simpler from the > one in Data.List but it also performs better. Here are some numbers from my > rather old ghc 6.8.1 running ubuntu on my box: > > *Main> length $ permutations [1..10] > 3628800 > (10.80 secs, 2391647384 bytes) > *Main> length $ perm [1..10] > 3628800 > (8.58 secs, 3156902672 bytes)
But you compare *interpreted* code here, that's not what counts. Prelude Perms> length $ perm [1 .. 10] 3628800 (1.20 secs, 1259105892 bytes) Prelude Perms> length $ permutations [1 .. 10] 3628800 (0.56 secs, 551532668 bytes) Prelude Perms> length $ perm [1 .. 11] 39916800 (13.18 secs, 14651808004 bytes) Prelude Perms> length $ permutations [1 .. 11] 39916800 (4.30 secs, 5953485728 bytes) Apparently the library code is more amenable to the optimiser (note that the actual library is faster still: Prelude Data.List> length $ permutations [1 .. 10] 3628800 (0.49 secs, 551532812 bytes) Prelude Data.List> length $ permutations [1 .. 11] 39916800 (3.73 secs, 5953485816 bytes) I have no idea why). > > I would like to suggest to change the current implementation in Data.List > with the simpler one. Also, it would be nice to add variations and > combinations in the Data.List module. > > Cheers. _______________________________________________ Glasgow-haskell-users mailing list [email protected] http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
