Author: Uri Blass
Date: 21:47:40 05/09/01
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On May 09, 2001 at 22:02:48, Jeremiah Penery wrote: >On May 09, 2001 at 17:58:08, Uri Blass wrote: > >>The definition that I remember from university for O(1) is: >> >>f(n) is O(1) if there is a constant C such that |f(n)|<C for every finite n. >>(|f(n)| is the absulute value of f(n)). >> >>We learn from this definition that if n is bounded then f(n) is O(1) because you >>can choose C=1+max(|f(1)|,|f(2)...|f(n)|) >> >>An algorithm that help to solve only one problem that can be solved in a finite >>time is always O(1) by this definition. >>An algorithm that helps to solve a finite set of problems that everyone of them >>can be solved in a finite time is also O(1) by this definition. >> >>1)If you look at the problems search to depth n in chess then there is only a >>finite number of problems because searching to depth 9^(9^9) gives the same >>result as searching to depth 9^(9^9)+1 even without the 50 move rule. >> >>Conclusion:Searching to depth n in chess is O(1). > >No. The idea behind O (for tree-searching algorithms) is to find out how much >longer will it take to search from depth N to N+1. In this case 0 seconds because if N is 9^(9^9) and you searched depth N you also searched depth N+1. I agree that chess is practically exponentional because you cannot go to the big depthes that I described. This is my last post in this discussion and the fact that I stop to post does not say that I agree. I stop to post only because of the fact that people complain that it is off topic. Uri
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