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MathGroup Archive 1996

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Re: array ordered

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3178] Re: array ordered
  • From: Jorma.Virtamo at vtt.fi (Jorma Virtamo)
  • Date: Tue, 13 Feb 1996 02:29:16 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

TTCJ34A at prodigy.com (DR JOHN C ERB) wrote:
>
>  I have six pieces of plastic of thickness:
>   thick={0.48,0.71,1.41,3.45,5.61,13.49};
> 
> By using these in various combinations
> (i.e., 1 piece, 2 pieces,... 6 pieces),
> I can have: 
>       numberthick={1,2,3,4,5,6};
>       total = Apply[Plus,Map[Binomial[6,#]&,numbthick]];
>       total = 63
> 63 different thickness.
> 
> How can I use Mathematica to get an array, ordered by
> increasing thicknesses of plastic, giving the
> 63 different thicknesses, and combination of pieces
> needed to give each thickness?
> 

Here is one solution:

First, form a list of all possible piece combinations,

  In[1]:=  piececombs=Flatten[Array[List,{2,2,2,2,2,2},0],5]

  Out[1]=
   {{0, 0, 0, 0, 0, 0}, 
    {0, 0, 0, 0, 0, 1},   
    {0, 0, 0, 0, 1, 0}, 
    {0, 0, 0, 0, 1, 1}, 
    {0, 0, 0, 1, 0, 0}, 
    {0, 0, 0, 1, 0, 1}, 
    {0, 0, 0, 1, 1, 0},  etc

where 1 (0) means that a piece is (is not) used in the combination.
There are 64 combinations, not 63, since the empty combination is 
also included (of course, one can drop it by Drop[piececombs,1]).

Then prepend to each piece combination in the list its thickness and
finally sort the whole list:

  In[2]:= Sort[{Plus @@ (#*thick), #}& /@ piececombs]//MatrixForm

  Out[2]=
  0              {0, 0, 0, 0, 0, 0}
  0.48           {1, 0, 0, 0, 0, 0}
  0.71           {0, 1, 0, 0, 0, 0}
  1.19           {1, 1, 0, 0, 0, 0}
  ...
  ...
  23.96          {0, 0, 1, 1, 1, 1}
  24.44          {1, 0, 1, 1, 1, 1}
  24.67          {0, 1, 1, 1, 1, 1}
  25.15          {1, 1, 1, 1, 1, 1} 


-- Jorma Virtamo

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jorma Virtamo                      VTT Information Technology
phone: +358 0 456 5612             Telecommunications
fax:   +358 0 455 0115             P.O. Box 1202  
email: jorma.virtamo at vtt.fi        FIN-02044 VTT                        
web:   http://www.vtt.fi/tte/      Finland


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