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Re: count zeros in a number
*To*: mathgroup at smc.vnet.net
*Subject*: [mg121865] Re: count zeros in a number
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Wed, 5 Oct 2011 04:02:11 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*References*: <201110020636.CAA28027@smc.vnet.net> <j6brvm$8om$1@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
I'm guessing that I got zero because I ran some of the code with an
undefined x. My bad!
Correcting that, I find the esoteric method faster than your ancient,
outmoded ones:
x = 24^24*55^55;
Replace[IntegerDigits@x, {__, zeroes : 0 ..} :>
Length@{zeroes}] // Timing
{0.000198, 55}
(n = 0; While[GCD[x, 10^n] == 10^n, n++]; n - 1) // Timing
{0.000417, 55}
(n = 0; While[Mod[x, 10] == 0, (x = x/10; n++)]; n) // Timing
{0.000228, 55}
Bobby
On Tue, 04 Oct 2011 15:57:30 -0500, Richard Fateman
<fateman at eecs.berkeley.edu> wrote:
> 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
>
>
>
--
DrMajorBob at yahoo.com
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