Re: A list of numbers without "73"

*To*: mathgroup at smc.vnet.net*Subject*: [mg63023] Re: [mg63005] A list of numbers without "73"*From*: gardyloo <gardyloo at mail.wsu.edu>*Date*: Sun, 11 Dec 2005 04:56:45 -0500 (EST)*References*: <200512101103.GAA29418@smc.vnet.net> <439B2238.8040208@mail.wsu.edu>*Sender*: owner-wri-mathgroup at wolfram.com

gardyloo wrote: >Thomas Schmelzer wrote: > > > >>Experts, >> >>S(i) should be a list of positive integers without the substring "73". >> >>My code seems to be very inefficient. I multiply all numbers with 0 if they >>contain "73", sort the new list, make the union (remove double elements) and >>delete the first element. Therefore it is necessary to use an if statement >>in order not to delete the first element of the numbers 1-9. Any more >>sophisticated ideas? >> >>L := Table[k, {k, 1, 9}] >> >>S[i_] := S[i] = >>If[i == 1, L, >>Delete[Union[ >>Table[k*(1 - Boole[StringMatchQ[ToString[k], "*73*"]]), {k, >>10^(i - 1), 10^i - 1}]], 1]] >> >> >> >>Best >> >>Thomas >> >> >> > > Hi, Thomas, > > I don't know about the timing issues inherent with using Select >(does it check _each_ member of its enclosed list; might, perhaps, an if >statement for the power "i" used in Range be more efficient? I'm too >lazy to do rigorous checks), but this should work for you: > >S[i_] := Select[Range[10^(i - 1), 10^i - 1], #1 != 73 & ] > > >In[32]:= >$Version > >Out[32]= >5.2 for Linux (June 20, 2005) > > > Best of luck, > C.O. > OK, so I'm not quite that lazy. A quick logarithmic regression on fresh kernels gives the evaluation time for your function of roughly time(i) ~ Exp[-11.54+2.273 *i], in seconds. My (unrefined) function seems to be roughly 10x as fast (for exponents -- or values of i -- around 2 to 5), to around 7.5x as fast (for values of i around 8) , probably due to not having to do string-matching stuff. Regards, C.O.

**References**:**A list of numbers without "73"***From:*"Thomas Schmelzer" <thomas.???@balliol.ox.ac.uk>