[Haskell-cafe] Help with Bird problem 4.5.6: sequence of successive
maxima
R J
rj248842 at hotmail.com
Sun Mar 15 16:09:48 EDT 2009
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.
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