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Can a question on this site have a winner based on the lowest complexity? Each answer would require the code's complexity in Big-O notation, and the winner would be the first to submit an answer with the lowest (so, if three people submit answers with O(n), the first one wins).

I can't remember seeing any questions like this, so I am curious as to what the decision will be.

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This already exists, as the tag. From its wiki excerpt:

Fastest-algorithm competitions are won by the answer with the smallest asymptotic time complexity. For challenges based on actual runtime, use instead.

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  • \$\begingroup\$ I never noticed that before. Thanks before the reference! \$\endgroup\$ – erdekhayser Dec 23 '14 at 0:23

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