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MathGroup Archive 1996

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Re: array ordered

  • To: mathgroup at smc.vnet.net
  • Subject: [mg3180] Re: array ordered
  • From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
  • Date: Tue, 13 Feb 1996 02:29:37 -0500
  • Organization: University of Colorado, Boulder
  • Sender: owner-wri-mathgroup at wolfram.com

In article <4fhh6k$963 at dragonfly.wolfram.com>,
DR JOHN C ERB <TTCJ34A at prodigy.com> wrote:
>Greetings All;
>
> I have six pieces of plastic of thickness:
>  thick={0.48,0.71,1.41,3.45,5.61,13.49};
>
>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?

I'll give a solution using only the first 3 thicknesses as an example,
to save space.  The code should work for the longer list as well.

thick={0.48,0.71,1.41};

Outer[List, ##]& @@ Table[{0,1}, {Length[thick]}]
{{{{0, 0, 0}, {0, 0, 1}}, {{0, 1, 0}, {0, 1, 1}}}, 
  {{{1, 0, 0}, {1, 0, 1}}, {{1, 1, 0}, {1, 1, 1}}}}

Flatten[%, Length[thick]-1]
{{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, 
  {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}

combos = Drop[%, 1]
{{0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, 
  {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}

{#.thick, #}& /@ combos
{{1.41, {0, 0, 1}}, {0.71, {0, 1, 0}}, {2.12, {0, 1, 1}}, {0.48, {1, 0, 0}}, 
  {1.89, {1, 0, 1}}, {1.19, {1, 1, 0}}, {2.6, {1, 1, 1}}}

Sort[%]
{{0.48, {1, 0, 0}}, {0.71, {0, 1, 0}}, {1.19, {1, 1, 0}}, {1.41, {0, 0, 1}}, 
  {1.89, {1, 0, 1}}, {2.12, {0, 1, 1}}, {2.6, {1, 1, 1}}}


		Dave Wagner
		Principia Consulting
		(303) 786-8371
		dbwagner at princon.com
		http://www.princon.com/princon

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