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Re: Big O

Cross-posted to 2 groups.

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BartC wrote:
)
)
) "Gen" <g@g.com> wrote in message news:j8r6fg$ih7$1@dont-email.me...
)> I have program where the other loop runs 'n' times.
)> When i is 0 in the outer loop, the inner loop runs n times
)> When i is 1 in the outer loop, the inner loop runs n/2 times
)> When i is 2 in the other loop, the inner loop runs n/3 times.
)>
)> i.e. The inner loop runs n/(i+1) times.
)>
)> If I had express the complexity of this program in Big O notation,
)> what would it be?
)>
)> I am thinking it will be O(nlogn) - but I am not sure how to justify it 
)> because it's not exactly a binary algorithm.
)
) If you take any of those examples, if you make n ten times as big, will it 
) take ten times as long?

"any of those examples" ???  That's one single example.

) In that case it sounds like O(n). What's the relationship between i and n?

You seem to be assuming that this is a very simple question.
It is not.
This is an example of the kind of loop he's talking about:

for (i = 0; i < n; i++) {
  for (j = 0; j < (n/(i+1)); j++) {
    do_something();
  }
}

Given that there is no closed form for 1/1+1/2+1/3+...+1/(n-1)+1/n,
it's not trivial to prove that this is O(n lg n).


SaSW, Willem
-- 
Disclaimer: I am in no way responsible for any of the statements
            made in the above text. For all I know I might be
            drugged or something..
            No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

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Thread

Big O Gen <g@g.com> - 2011-11-02 16:06 +0530
  Re: Big O "BartC" <bc@freeuk.com> - 2011-11-02 10:56 +0000
    Re: Big O Willem <willem@toad.stack.nl> - 2011-11-02 11:26 +0000
      Re: Big O "BartC" <bc@freeuk.com> - 2011-11-02 11:39 +0000
      Re: Big O "Scott Fluhrer" <sfluhrer@ix.netcom.com> - 2011-11-02 10:28 -0400
        Re: Big O gwowen <gwowen@gmail.com> - 2011-11-02 09:08 -0700
  Re: Big O gwowen <gwowen@gmail.com> - 2011-11-02 04:15 -0700
  Re: Big O Willem <willem@toad.stack.nl> - 2011-11-02 11:16 +0000
  Re: Big O Gen <g@g.com> - 2011-11-02 18:43 +0530

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