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Subject: Re: Big-O notation - correction

Author: Eugene Nalimov

Date: 11:30:36 05/09/01

Go up one level in this thread


Input in our case is (position, depth), and the question is "how longer will
take to evaluate (position, depth+1)"?

Eugene

On May 09, 2001 at 14:11:25, Ricardo Gibert wrote:

>On May 09, 2001 at 14:08:10, Ricardo Gibert wrote:
>
>>On May 09, 2001 at 14:04:55, Eugene Nalimov wrote:
>>
>>>Uri, there is branch of the mathematics (not even computer science, just
>>>ordinary mathematics) that studies the complexity of algorithms. Algorithms were
>>>used in mathematics long before computers appeared, for example GCD algorithm
>>>was known to the classic greeks.
>>>
>>>*Very* rude explanation of big-O notation is: you have the algorithm that
>>>require M operations (or steps, or machine instructions, or clock cycles, etc.)
>>>when input in N elements long. You are increasing length of the input; how much
>>>operations will be necessary now? That has *nothing* to do with the fact that
>>>majority of practically used algorithms will terminate in finite number of steps
>>>when input is finite.
>>>
>>>Eugene
>>
>>
>
>
>But [in chess] the the length of the input does not increase and that's the
>whole point.
>
>
>>
>>
>>>
>>>On May 09, 2001 at 13:37:58, Uri Blass wrote:
>>>
>>>>On May 09, 2001 at 13:23:25, Dann Corbit wrote:
>>>>
>>>>>On May 09, 2001 at 13:18:52, Uri Blass wrote:
>>>>>
>>>>>>On May 09, 2001 at 11:27:46, Dann Corbit wrote:
>>>>>>
>>>>>>>On May 09, 2001 at 10:12:30, Ricardo Gibert wrote:
>>>>>>>
>>>>>>>>On May 09, 2001 at 02:00:25, Dann Corbit wrote:
>>>>>>>>
>>>>>>>>>For those of you who don't want to perform your own web search, just choose one
>>>>>>>>>of these:
>>>>>>>>>
>>>>>>>>>http://hissa.nist.gov/dads/HTML/bigOnotation.html
>>>>>>>>>http://bio5495.wustl.edu/textbook-html/node15.html
>>>>>>>>>http://umastr.math.umass.edu/~holden/Math136-99_projects/Amstutz-OBoyle-Petravage/big-o.html
>>>>>>>>>http://www.eecs.harvard.edu/~ellard/Q-97/HTML/root/node8.html
>>>>>>>>>http://classes.monterey.edu/CST/CST338-01/world/BigO.html
>>>>>>>>>http://shalim.csustan.edu/~john/Classes/CS3100_DataStructures/Previous_Semesters/1999_04_Fall/Examples/big-O
>>>>>>>>>
>>>>>>>>>CS:201, FCOL!
>>>>>>>>
>>>>>>>>Big-O notation is used to describe asymtotic behavior. It commonly used to
>>>>>>>>describe the "running time" of an algorithm. If an algorithm is O(f(n)), n is
>>>>>>>>understood to be a finite, but *unbounded*. (For some reason, "unbounded" gets
>>>>>>>>confused with infinity. This is an error, but let's not get into that. It isn't
>>>>>>>>relevant here)
>>>>>>>>
>>>>>>>>In chess, n in is bounded. This is a critical distinction, that means chess is
>>>>>>>>*not* NP.
>>>>>>>
>>>>>>>GREAT!  Then it's computable.  What's the answer, win-loss-draw?
>>>>>>>;-)
>>>>>>
>>>>>>I see no point in continuing to argue.
>>>>>>The question is simply question of definition.
>>>>>>I did not say that it is easy to solve.
>>>>>>
>>>>>>I use the definition of NP only for problems with n that is not bounded
>>>>>>otherwise the mathematical definition say that it is O(1)(there is a constant
>>>>>>and the only problem is that it is too large)
>>>>>>
>>>>>>I can agree that chess is practically O(exp(n)) and not polynomial for practical
>>>>>>purposes but it does not change the fact that by mathematical definition it is
>>>>>>O(1).
>>>>>
>>>>>This is simply wrong.  I guess we are at an impasse.
>>>>>
>>>>>>You can say that Sorting is also O(1) from theoretical point of view if you look
>>>>>>at sorting that is done by a computer.
>>>>>
>>>>>Show me any algorithms book that says any sorting algorithm is O(1).
>>>>
>>>>The sorting from theoretical point of view is not O(1) because the size of the
>>>>input is not bounded.
>>>>Sorting done by a computer has bounded size and every problem of bounded size is
>>>>O(1) by the definition that I know.
>>>>
>>>>A problem can be O(n) only if n is not bounded by a finite bound by the
>>>>definition that I use.
>>>>
>>>>I look at sorting from mathematical point of view and not from computer point of
>>>>view and this is the reason that I said that it is not O(1).
>>>>
>>>>Uri



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