R J schrieb:
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".
Hi,
this problem is a variant of
http://en.wikipedia.org/wiki/Longest_increasing_subsequence
discussed about a year ago:
http://www.mail-archive.com/haskell-cafe@haskell.org/msg39784.html
http://www.mail-archive.com/haskell-cafe@haskell.org/msg39844.html
In the latter mail, Chris Kuklewicz presents an (efficient)
implementation. To solve the problem you stated, simply reuse `lnds`:
> -- ssm [3, 1, 3, 4, 9, 2, 9, 10, 7] = [3,4,9,10]
> ssm (x:xs) = x : lnds (filter (> x) xs)
benedikt
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.
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