Re: count zeros in a number

*To*: mathgroup at smc.vnet.net*Subject*: [mg121859] Re: count zeros in a number*From*: Richard Fateman <fateman at eecs.berkeley.edu>*Date*: Wed, 5 Oct 2011 04:01:07 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201110020636.CAA28027@smc.vnet.net> <j6brvm$8om$1@smc.vnet.net> <201110040530.BAA20698@smc.vnet.net> <op.v2t544pxtgfoz2@bobbys-imac.local>

On 10/4/2011 9:44 AM, DrMajorBob wrote: > There's nothing "esoteric" about IntegerDigits, Replace, or Repeated, > as in: > > x = 24^24*55^55; > Replace[IntegerDigits@x, {__, zeroes : 0 ..} :> > Length@{zeroes}] // Timing > > {0.000185, 55} My feeling is that these ARE esoteric. A person just introduced to Mathematica would probably not encounter IntegerDigits, Repeated, or patterns other than the trivial one used in pseudo function definitions as f[x_]:= x+1. > > If we wanted brute-force arithmetic, we might use Fortran. > > Your suggested solutions are NOT greatly hindered by "the slow > implementation of looping constructs in Mathematica", on the other hand: > > (n = 0; While[GCD[x, 10^n] == 10^n, n++]; n - 1) // Timing > > {0.000029, 0} huh? I got {0., 55}. Perhaps my computer is faster or has a lower resolution timer, but we should both get 55. > > (n = 0; While[Mod[x, 10] == 0, (x = x/10; n++)]; n) // Timing > > {0.000018, 0} I mention the slow implementation of looping constructs simply to warn people that if you can resolve your computation by simple composition of built-in functions e.g. F[G[H[x]]] and don't rely on Mathematica to efficiently execute loops written as While[] For[] etc, you are probably going to run faster. Let Mathematica's operation on compound objects like lists do the job. Length[] is a lot faster than counting with a While etc. In my timings, doing the operations 1000 times.. Do[.....,{1000}]//Timing I found that my solutions were about 10X faster than the IntegerDigits one, on this particular value of x. Fortran can't be used unless you manage arbitrary precision integers... RJF

**References**:**count zeros in a number***From:*dimitris <dimmechan@yahoo.com>

**Re: count zeros in a number***From:*Richard Fateman <fateman@cs.berkeley.edu>