Re: array ordered
- To: mathgroup at smc.vnet.net
- Subject: [mg3190] Re: array ordered
- From: espen.haslund at fys.uio.no (Espen Haslund)
- Date: Tue, 13 Feb 1996 02:31:22 -0500
- Organization: Universitet i Oslo
- Sender: owner-wri-mathgroup at wolfram.com
In article <4fhh6k$963 at dragonfly.wolfram.com>, TTCJ34A at prodigy.com says...
>
>Greetings All;
>
> 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?
>
>Thank you for any help
>
Greetings John;
Below is one possible solution. I am sure
that more elegant (and general) methods are available.
However, this solution demonstrates a nice thing about
Mathematica: Even if you do not know how to do a
thing properly, you can usually Do[ it anyway.
Hope this is of some help.
- Espen
take2[list_] :=
Module[{ll = Length[list], res={}},
Do[AppendTo[res, Union[list[[{i, j}]] ] ], {i,1,ll},{j,1,ll}];
Union[res]
]
take3[list_] :=
Module[{ll = Length[list], res={}},
Do[AppendTo[res, Union[list[[{i, j, k}]] ] ],{i,1,ll},
{j,1,ll},{k,1,ll}];
Union[res]
]
getThickness[list_] :=
Module[{res, res1},
res = take3[list];
res1 = Map[Complement[list, #] &, take2[list] ];
res = Join[res, res1, {list}];
Do[res[[i]] = {Plus @@ res[[i]], res[[i]]}, {i, 1, Length[res]}];
Sort[res]
]
thick={0.48,0.71,1.41,3.45,5.61,13.49}
PaddedForm[ColumnForm[getThickness[thick] ], {4,2} ]
(* - resulted in -
//PaddedForm= { 0.48, { 0.48}}
{ 0.71, { 0.71}}
{ 1.19, { 0.48, 0.71}}
{ 1.41, { 1.41}}
{ 1.89, { 0.48, 1.41}}
{ 2.12, { 0.71, 1.41}}
{ 2.60, { 0.48, 0.71, 1.41}}
{ 3.45, { 3.45}}
{ 3.93, { 0.48, 3.45}}
{ 4.16, { 0.71, 3.45}}
{ 4.64, { 0.48, 0.71, 3.45}}
{ 4.86, { 1.41, 3.45}}
{ 5.34, { 0.48, 1.41, 3.45}}
{ 5.57, { 0.71, 1.41, 3.45}}
{ 5.61, { 5.61}}
{ 6.05, { 0.48, 0.71, 1.41, 3.45}}
{ 6.09, { 0.48, 5.61}}
{ 6.32, { 0.71, 5.61}}
{ 6.80, { 0.48, 0.71, 5.61}}
{ 7.02, { 1.41, 5.61}}
{ 7.50, { 0.48, 1.41, 5.61}}
{ 7.73, { 0.71, 1.41, 5.61}}
{ 8.21, { 0.48, 0.71, 1.41, 5.61}}
{ 9.06, { 3.45, 5.61}}
{ 9.54, { 0.48, 3.45, 5.61}}
{ 9.77, { 0.71, 3.45, 5.61}}
{ 10.25, { 0.48, 0.71, 3.45, 5.61}}
{ 10.47, { 1.41, 3.45, 5.61}}
{ 10.95, { 0.48, 1.41, 3.45, 5.61}}
{ 11.18, { 0.71, 1.41, 3.45, 5.61}}
{ 11.66, { 0.48, 0.71, 1.41, 3.45, 5.61}}
{ 13.49, { 13.49}}
{ 13.97, { 0.48, 13.49}}
{ 14.20, { 0.71, 13.49}}
{ 14.68, { 0.48, 0.71, 13.49}}
{ 14.90, { 1.41, 13.49}}
{ 15.38, { 0.48, 1.41, 13.49}}
{ 15.61, { 0.71, 1.41, 13.49}}
{ 16.09, { 0.48, 0.71, 1.41, 13.49}}
{ 16.94, { 3.45, 13.49}}
{ 17.42, { 0.48, 3.45, 13.49}}
{ 17.65, { 0.71, 3.45, 13.49}}
{ 18.13, { 0.48, 0.71, 3.45, 13.49}}
{ 18.35, { 1.41, 3.45, 13.49}}
{ 18.83, { 0.48, 1.41, 3.45, 13.49}}
{ 19.06, { 0.71, 1.41, 3.45, 13.49}}
{ 19.10, { 5.61, 13.49}}
{ 19.54, { 0.48, 0.71, 1.41, 3.45, 13.49}}
{ 19.58, { 0.48, 5.61, 13.49}}
{ 19.81, { 0.71, 5.61, 13.49}}
{ 20.29, { 0.48, 0.71, 5.61, 13.49}}
{ 20.51, { 1.41, 5.61, 13.49}}
{ 20.99, { 0.48, 1.41, 5.61, 13.49}}
{ 21.22, { 0.71, 1.41, 5.61, 13.49}}
{ 21.70, { 0.48, 0.71, 1.41, 5.61, 13.49}}
{ 22.55, { 3.45, 5.61, 13.49}}
{ 23.03, { 0.48, 3.45, 5.61, 13.49}}
{ 23.26, { 0.71, 3.45, 5.61, 13.49}}
{ 23.74, { 0.48, 0.71, 3.45, 5.61, 13.49}}
{ 23.96, { 1.41, 3.45, 5.61, 13.49}}
{ 24.44, { 0.48, 1.41, 3.45, 5.61, 13.49}}
{ 24.67, { 0.71, 1.41, 3.45, 5.61, 13.49}}
{ 25.15, { 0.48, 0.71, 1.41, 3.45, 5.61, 13.49}}
*)
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