Am Sonntag, 15. März 2009 21:09 schrieb R J:
This Bird problem vexes me, in the first instance because it doesn't seem to specify a unique solution:
Given a list xs = [x_1, x_2, . . . , x_n], the sequence of successive maxima "ssm xs" is the longest subsequence [x_j1, x_j2, x_j3..x_jk] such that j_1 = 1 and j_m < j_n => x_jm < x_jn. For example, xs = [3, 1, 3, 4, 9, 2, 10, 7] => ssm xs = [3, 4, 9, 10]. Define "ssm" in terms of "foldl".
From this specification, I infer:
ssm [] = [] ssm [1] = [1] ssm [1, 2, 3] = [1, 2, 3] ssm [1, 0, 3, 2] = [1, 3]
However, what is ssm [1,0,100,2,3,4,5]? Is it [1, 100] or [1, 2, 3, 4, 5]? I think the latter, but am not certain. Whichever it is, what's the solution?
Thanks.
Not particularly efficient, but module SSM where import Data.List (maximumBy) import Data.Ord ssm :: Ord a => [a] -> [a] ssm = reverse . maximumBy (comparing length) . foldl comb [[]] where comb [[]] a = [[a]] comb lists a = do xs@(h:_) <- lists if h < a then [xs,a:xs] else [xs] I think it is impossible to implement ssm as foldl f z without any post-processing and since foldl can't foresee what comes in the remainder of the list, you must keep several candidates around. You can probably make it more efficient by removing all lists lst@(h:_) where there's a longer list with head <= h or an equally long list with head < h in the store (but doing that efficiently is not trivial).