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 Post subject: Running TimesPosted: Thu, 10 Mar 2011 14:15:50 UTC
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Hi all.

I'm a bit stuck on this question.

So an algorithm A has a running time in and in .

State whether and why it is consistent or inconsistent with the claim mentioned above for the following statements.

a) in
b) in
c) in
d) in

a) no. because in , grows faster
b) no. same as above.
c) yes. does grow at the same rate as , and is faster than .
d) no. does not grow at . it is faster.

and i on the right track?

Thanks.

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 Post subject: Re: Running TimesPosted: Thu, 10 Mar 2011 14:28:34 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
asa.hoshi wrote:
Hi all.

I'm a bit stuck on this question.

So an algorithm A has a running time in and in .

State whether and why it is consistent or inconsistent with the claim mentioned above for the following statements.

a) in
b) in
c) in
d) in

a) no. because in , grows faster
b) no. same as above.
c) yes. does grow at the same rate as , and is faster than .
d) no. does not grow at . it is faster.

and i on the right track?

Thanks.

For the last one, what is "it"? If you mean the algorithm, then no, you're wrong, the algorithm does not grow faster it IS faster, which means the complexity is slower, i.e. shorter run-time. Be careful with how you use "faster" when talking about asymptotics.

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 Post subject: Posted: Thu, 10 Mar 2011 22:01:12 UTC
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i think i meant to say that n^3 grows faster then n^2 for q.d). And Cos they dont grow at the same speed, ans is no. Then is that right?

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 Post subject: Posted: Thu, 10 Mar 2011 22:19:37 UTC
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Location: Austin, TX
asa.hoshi wrote:
i think i meant to say that n^3 grows faster then n^2 for q.d). And Cos they dont grow at the same speed, ans is no. Then is that right?

In particular it's because isn't between the two bounds (it's not )

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 Post subject: Posted: Mon, 14 Mar 2011 10:39:29 UTC
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Joined: Thu, 11 May 2006 11:24:10 UTC
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asa.hoshi wrote:
i think i meant to say that n^3 grows faster then n^2 for q.d). And Cos they dont grow at the same speed, ans is no. Then is that right?

In particular it's because isn't between the two bounds (it's not )
i think im confusing myself here.

but for a) in .

Okay, so i know that comparing and . Obviously, grows faster. And is faster than .

So, having said that is it consistent with the fact that the alrogithm whose running time is in and ? Because it is within the bounds of both running times. Does that make sense?

Or... is it because, the question says, no faster than , but the algorithm can run faster than and up to ? So answer is inconsistent.

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 Post subject: Posted: Mon, 14 Mar 2011 17:47:11 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12098
Location: Austin, TX
asa.hoshi wrote:
asa.hoshi wrote:
i think i meant to say that n^3 grows faster then n^2 for q.d). And Cos they dont grow at the same speed, ans is no. Then is that right?

In particular it's because isn't between the two bounds (it's not )
i think im confusing myself here.

but for a) in .

Okay, so i know that comparing and . Obviously, grows faster. And is faster than .

So, having said that is it consistent with the fact that the alrogithm whose running time is in and ? Because it is within the bounds of both running times. Does that make sense?

Or... is it because, the question says, no faster than , but the algorithm can run faster than and up to ? So answer is inconsistent.

The first conclusion is correct. You should recall that the big O means something akin to and means something akin to

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