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November 8th, 2009, 05:05 PM  #1 
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Which function is bigger
Hopefully this is the correct forum for this. Let . I have an algorithm that I need to show makes at most comparisons, where is related to the input size. I have determined that the algorithm makes comparisons, so I can increase its number of comparisons to . So the only thing different is vs . Is it true that ? If that's the case then I arrive at the required result. I have been graphing the functions using an online applet that seems to show they are "identical", but I can't determine if the first one is less than or equal to the second one. This specific question I am working on didn't mention asymptotic bounds, it's more of finding the exact number (otherwise it's just ). Thanks 
November 8th, 2009, 05:56 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 16,942 Thanks: 1253 
If n = 3, but 
November 8th, 2009, 07:01 PM  #3 
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Re: Which function is bigger
Thanks for your response. So basically I am stuck with what I have, and have to look for a different way? I.e., what I have doesn't satisfy the requirement, because right now it performs (slightly) more comparisons. 
November 8th, 2009, 10:13 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 16,942 Thanks: 1253 
Very possibly. It's difficult to say more unless you disclose all the details.

November 9th, 2009, 09:39 AM  #5 
Member Joined: Sep 2008 Posts: 41 Thanks: 0  Re: Which function is bigger
I think the only remaining details is the algorithm itself. Ill probably try and ask for hints from classmates or the professor. I just wanted to get working on it on the weekend was over, and didnt have those resources until then. If youre interested, the algorithm is to find the 3rd largest of a list of distinct elements, for example distinct natural numbers. 

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