Many thanks. I don't *think* it's ever been as bad as O(mn) (I'm pretty
sure it's no worse than O(m log m log n) and it may well be better), but
it's certainly not great for time and it's definitely not great for space.
I believe both of your versions are essentially based on fast
exponentiation, which was going to be my fall-back position barring
something more magically good taking advantage of the tree structure
somehow. I know there are some fancy versions of fast exponentiation to
minimize multiplications, but any version thereof would be better than the
current approach.
On Wed, Nov 19, 2014 at 11:45 AM, Ross Paterson
On Tue, Nov 18, 2014 at 04:49:23PM -0500, David Feuer wrote:
I'd like to define (*>) and (>>) for Data.Seq.Seq in a "clever" way, like replicate, but I'm a bit stuck. It kind of looks like this is the purpose behind the applicativeTree function, which bills itself as a generalization of replicateA, but something seems to have gotten stuck and the only time I see applicativeTree actually used is to define replicateA. With all the fancy nesting, I'm a bit lost as to how to go about this, and having only one example doesn't really help. Can someone help give me a clue?
I don't think applicativeTree will do the job -- it assumes the argument is a 2-3 tree (not a finger tree). The best I can think of is
xs *> ys = replicateSeq (Seq.length xs) ys
-- Concatenate n copies of xs replicateSeq :: Int -> Seq a -> Seq a replicateSeq n xs | n == 0 = empty | even n = nxs | otherwise = xs >< nxs where nxs = replicateSeq (n `div` 2) (xs >< xs)
I think it's O(log m*(log m + log n)), where m and n are the lengths of the two sequences, which is certainly an improvement on O(mn).
Another way of doing replicateSeq would be
replicateSeq :: Int -> Seq a -> Seq a replicateSeq n xs | n == 0 = empty | even n = half >< half | otherwise = xs >< half >< half where half = replicateSeq (n `div` 2) xs
I'm not sure which would give the most sharing. _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe