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Given a set of positive integers, not greater than 100000, how can we find the maximal subset such that no three numbers form an Arithmetic progression?

I am looking for some algorithmic approach. If the problem is NP complete, I would like corresponding transformation. Any kind of heuristics will help!

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closed as not constructive by Andrew, Martin, O.L., Daniel Rust, Lord_Farin Jun 15 '13 at 10:51

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There is a claim from this user that "This problem is from currently going on competition on codechef and should be closed!" –  Zev Chonoles Jun 15 '13 at 9:59

1 Answer 1

Transform the sequence into a sequence of differences:

Eg.: if your original sequence is 1, 3, 8, 7, 7 then the transformed sequence is 2, 5, -1, 0.

Then look for the maximum-length substring that contains no repeating values:

Do a linear-time scan of the sequence to mark the begin and end points of such repeating values as you go along. Then, do a second linear search for the maximum-length subsequence between a pair of end-begin marks that appear in this order without a third mark in between. The algorithm is linear. Its details should be straightforward.

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how is this algorithms correct? –  user2255279 Jun 15 '13 at 8:12

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