Re: generating all combinations.
- To: mathgroup at smc.vnet.net
- Subject: [mg22422] Re: [mg22395] generating all combinations.
- From: "Mark Harder" <harderm at ucs.orst.edu>
- Date: Wed, 1 Mar 2000 00:40:20 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
Wen-Feng and everyone,
I think what Wen-Feng is trying to do is construct the n-fold
CartesianProduct of a set, which is the list of all ordered n-element lists
of members of the set. The Combinatorica package contains an attempt at a
CartesianProduct function, but it only works correctly when applied to a
pair of sets. Reiterating this function with a prior result does *not*
result in a CartesianProduct of higher power (in Mathematica 3.0.x). Load
DiscreteMath`Combinatorica` and try the following to see the problem:
set={1,2};
CartesianProduct[set,set]
CartesianProduct[set,%]
The 2-fold CP is o.k., but the 3-fold product should be a list of 8
triples, and it isn't. In order to get the correct answer, you have to
Flatten & re- Partition, like Wen-Feng has done, and I couldn't figure out
how to do that automatically for the general n-fold case. Somebody at
Wolfram should fix this.
Here is the work-around that I found. The recursive function ExponentialSet
is a little long, but using it is easy:
<<DiscreteMath`Combinatorica`
ClearAll[ExponentialSet];
ExponentialSet[set_List,1]:= set;
ExponentialSet[set_List,2]:=CartesianProduct[set,set];
ExponentialSet[set_List,n_]:=
Map[Flatten,CartesianProduct[set,ExponentialSet[set,n-1] ] ];
eg.
In[67]:= set2={1,2};
exponentialSet[set2,3]
Out[67]=
{{1,1,1},{1,1,2},{1,2,1},{1,2,2},{2,1,1},{2,1,2},{2,2,1},{2,2,2}}
OK?
-mark harder
harderm at ucs.orst.edu
-----Original Message-----
From: Wen-Feng Hsiao <d8442803 at student.nsysu.edu.tw>
To: mathgroup at smc.vnet.net
Subject: [mg22422] [mg22395] generating all combinations.
>Dear all,
>
>I would like to generate all the combinations n-digit lists, which can
>vary between a certain range and duplications are allowed. The three
>digits with range between -2 to 2 is the following:
>
>allcomb =
> Table[{i, j, k}, {i, -2, 2}, {j, -2, 2}, {k, -2, 2}];
>fltcomb = Partition[Flatten[allcomb], 3];
>
>Is there a more succinct way to do that? If I would like to expand the
>code to 10 digits, the code would looks clumsy.
>
>Thanks for your help.
>
>Wen-Feng
>
>