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MathGroup Archive 2002

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Re: A friendly challenge: Generalized Partition

  • To: mathgroup at smc.vnet.net
  • Subject: [mg34905] Re: [mg34858] A friendly challenge: Generalized Partition
  • From: Andrzej Kozlowski <andrzej at platon.c.u-tokyo.ac.jp>
  • Date: Wed, 12 Jun 2002 02:15:41 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Here is my first (and only) attempt, which probably does not quite match 
yours but comes close enough (considering the amount of time I can spare 
for this).


kk[ls_, t_] :=
   With[{w = FoldList[Plus, 0, t]},
     Map[Take[ls, #] &, Transpose[{Drop[w, -1] + 1, Rest[w]}]]]


Tests on my 400 mghz PowerBook G4:

In[3]:=
a = Range[2000];

In[4]:=
b = Table[Random[Integer, {1, 20}], {150}];

In[5]:=
First[Timing[Do[gg[a, b], {100}]]]

Out[5]=
6.24 Second

In[6]:=
First[Timing[Do[kk[a, b], {100}]]]

Out[6]=
0.35 Second

Since gg was somewhat faster than on your machine I assume that my kk is 
slower than your function.

Andrzej




On Tuesday, June 11, 2002, at 06:00  PM, Mr. Wizard wrote:

> In the 4.1 help browser, in Further Examples under Take, there is code
> for a generalized partition function, called gg.  This code is
> somewhat long and extremely slow.  I challenge you to duplicate the
> functionality of this code (ignoring the ggCheckArgs condition), while
> making it 1) as sort as possible, and/or 2) as fast as possible.
>
> Your function must be in good form, leaving no stray assignments, i.e.
> using the appropriate scoping construct(s).
>
> For efficiency testing, I will use (where func is your function):
>
> a = Range[2000];
> b = Table[Random[Integer, {1, 20}], {150}];
> First[Timing[Do[func[a, b], {100}]]]
>
> I will post my versions after a little while.  For reference, on my
> machine, the function from the help files, omitting the ggCheckArgs
> condition, takes 8 seconds; my fastest version takes 0.33 seconds.  My
> shortest version is 44 characters in length, and takes 0.94 seconds.
>
> Good luck!
>
> Paul
>
>
>
>
Andrzej Kozlowski
Toyama International University
JAPAN
http://platon.c.u-tokyo.ac.jp/andrzej/



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