Author: Uri Blass
Date: 14:53:30 12/19/01
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On December 19, 2001 at 17:32:24, Gustavo Pereira wrote: >On December 19, 2001 at 16:57:46, Michel Langeveld wrote: > >>Problem = 1 - ( 16777216! / (16746008! * 16777216 ^ 31208) ) >> >>16777216 = Number of records in my hashtable >>31208 = Number of nodes searched >> >>Windows calculator says BOOM. >> >>If Problem > 0.5 then I've spend 15 hours debugging for nothing :-) > >If you simplify you get > >1- (31208!/16777216^31208) > >Now, 31208/16777216 is the biggest term in the division, which is 0.00186014 >and the other 31207 multiplications are smaller. >So your result is as close to 1 as possible. No You assume that x!/(x-y)!=y! to get it. It is not correct you have 1-(16777215/16777216)*(16777214/16777216)*....(16746009/16777216) The smallest number here is 1-31207/16777216 I agree that it is bigger than 1/2 because 31207 is clearly bigger than sqrt(16777216) so most of the numbers here are bigger than x=1-(1/sqrt(16777216)) It means that the number without the 1- is smaller than x^sqrt(16777216) that is close to 1/e. and 1 minus the expression is bigger than 1-(1/e) that is bigger than 1/2. Uri
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