# Re: Pattern matching more than once

• To: mathgroup@smc.vnet.net
• Subject: [mg12096] Re: Pattern matching more than once
• From: Paul Abbott <paul@physics.uwa.edu.au>
• Date: Sat, 25 Apr 1998 01:30:28 -0400
• Organization: University of Western Australia
• References: <6hjqaa\$2kj@smc.vnet.net>

```ASARI Hirotsugu wrote:

> I have been stuck with the following problem for about 10 days.  I can't
> think of an elegant solution.
>
> Input: Two lists, from some universal set Output: Many "spliced" lists
> obtained from the input.
>
> e.g.    {{a,b,c},{d,e,f}} --> {{a,b,c},{d,e,f}} (no common element)
>
>         {{a,b,c},{d,b,f}} --> {{a,b,c},{d,b,f},{a,b,f},{d,b,c}}
>
>         {{a,b,c,d,e},{f,b,g,d,h}} -->
>                         {{a,b,c,d,e},{a,b,c,d,h},{a,b,g,d,e},{a,b,g,d,h},
>                          {f,b,c,d,e},{f,b,c,d,h},{f,b,g,d,e},{f,b,g,d,h}}

I think that the following code:

In[1]:=extendList[l_List]:= Module[{tr=Union/@Transpose[l]},
If[tr==Transpose[l],l,tr=Outer[List,Sequence@@tr];
Flatten[tr,Length[Dimensions[tr]]-2]]]

which relies on Transpose (to pair up elements from each list) Union (to
check for common elements) and Outer (to construct all allowed
combinations) does what you want:

In[2]:= extendList[{{a,b,c},{d,e,f}}] Out[2]= {{a,b,c},{d,e,f}}
In[3]:= extendList[{{a, b, e}, {d, b, f}}] Out[3]=
{{a,b,e},{a,b,f},{d,b,e},{d,b,f}} In[4]:=
extendList[{{a,b,c,d,e},{f,b,g,d,h}}] Out[4]=
{{a,b,c,d,e},{a,b,c,d,h},{a,b,g,d,e},{a,b,g,d,h},
{f,b,c,d,e},{f,b,c,d,h},{f,b,g,d,e},{f,b,g,d,h}}

I also feel that there should be a cleverer pattern-matching solution,
probably using ReplaceList ...

Cheers,
Paul

____________________________________________________________________
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907
mailto:paul@physics.uwa.edu.au  AUSTRALIA
http://www.pd.uwa.edu.au/~paul

God IS a weakly left-handed dice player
____________________________________________________________________

```

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