# Re: Pattern matching more than once

```Hi Asari,

I hope I understood what you are interested in.

extent[{x__,y_},{y_,z__}]={x,y,z};

extent[{x__?AtomQ,y_},li1:{__List}]:=
With[{li2=Cases[li1,{y,__}]},If[li2=={},{x,y}, extent[{x,y},#]&/@li2]];

extent[li1:{__List},li2:{__List}]:=
Cases[extent[#,li2]&/@li1,{__?AtomQ},\[Infinity]]

fu[li1_,li2_]:=  Module[{li3=Intersection[li1,li2],aux},

aux=Split[#,UnsameQ]&/@({li1,li2}/.(x_/;MemberQ[li3,x]->Sequence[x,x]));

FixedPoint[extent[#,Union@@Rest/@aux]&,First/@aux]]

aux doubles the common elements and then splits (with UnsameQ) between
those elements, producing segments with ends where crossing can take
place. FixedPoint extents---beginning with the first segments of the
two lists---until there is no more extension possible.

I supposed you were interested in all possible  chains, not only the
maximal ones.

J|rgen

-----Original Message-----
From: ASARI Hirotsugu <asari@math.uiuc.edu> To: mathgroup@smc.vnet.net
Subject: [mg12060] [mg11991] Pattern matching more than once

>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 will regard the input as list of chains (totally ordered set) coming
>from a partially ordered set, and I would like to extend these chains
>as much as possible.  If there is at most one common element in the
>inputs, the following will do:
>
>extendList[{list1:{pre1___,x_,post1___},list2:{pre2___,x_,post2___}}]:=
> {list1,list2,{pre1,x,post2},{pre2,x,post1}};
>
>The problem is that when the lists have more than one common element,
>the second common element will not be considered at all.  I suppose I
>could just write, for instance,
>
>extendList2[{list1:{pre1___,x_,mid1___,y_,post1___},
> list2:{pre2___,x_,mid2___,y_,post2___}}]:=
> Union[
> {list1,{pre1,x,mid1,y,post2},{pre1,x,mid2,y,post1},
> {pre1,x,mid2,y,post2},list2,{pre2,x,mid1,y,post1},
> {pre2,x,mid1,y,post2},{pre2,x,mid2,y,post1}}]; But this is very ugly.
>
>I suppose I could write some For[] loop through
>Intersection[list1,list2], but I would rather avoid it if I could.
>
>Any help would be appreciated.
>
>--
>ASARI Hirotsugu                 //   http://www.math.uiuc.edu/~asari/
>finger://math.uiuc.edu/asari   //    ph://ns.uiuc.edu/asari
> "We are what we pretend to be, so we must be careful
> about what we pretend to be." --Kurt Vonnegut
>

```

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