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Re: 1-liner wanted

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121676] Re: 1-liner wanted
  • From: "Oleksandr Rasputinov" <oleksandr_rasputinov at hmamail.com>
  • Date: Sun, 25 Sep 2011 05:42:13 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <j5hdfe$7j5$1@smc.vnet.net>

On Fri, 23 Sep 2011 08:45:50 +0100, Kent Holing <KHO at statoil.com> wrote:

> Let's assume we have a list of elements of the type {x,y,z} for x, y and  
> z integers. And, if needed we assume x < y < z. We also assume that the  
> list contains at least 3 such triples.
>
> Can Mathematica easily solve the following problem? To detect at least  
> three elements from the list of the type {a,b,.}, {b,c,.} and {a,c,.}? I  
> am more intereseted in an elegant 1-liner than computational efficient  
> solutions.
>
> Example:
> Givenlist ={1,2,3},{2,4,5],{6,7,8},{1,4,6},{7,8,9},{11,12,13}};
> should return
> {{1,2,3},{2,4,5},{1,4,6}}
>
> Kent Holing,
> Norway
>

The following is a brute-force approach; while short and easy to  
understand it is far from computationally efficent. As the concept of a  
line of code is not very well defined in Mathematica, I will leave it to  
you to decide whether or not it constitutes a one-liner.

f[list_] := ReplaceList[
  list,
  Apply[
   Alternatives,
   Permutations[
    {f:{a_, b_, _}, g:{b_, c_, _}, h:{a_, c_, _}},
    {3}
   ] /. {f_, g_, h_} :> {___, f, ___, g, ___, h, ___}
  ] :> {f, g, h}
]

list = {
  {1, 2, 3}, {2, 4, 5}, {6, 7, 8},
  {1, 4, 6}, {7, 8, 9}, {11, 12, 13}
};

f[list]

gives

{{{1, 2, 3}, {2, 4, 5}, {1, 4, 6}}}

which is a list of instances of the required sequence of items. In this  
case there is only one element in the list returned because there is only  
one possibility for the given input. For other lists multiple matches may  
be possible. Trying it on a slightly longer list:

f@RandomInteger[{0, 9}, {10, 3}]

gives

{
  {{6, 0, 2}, {0, 3, 4}, {6, 3, 1}},
  {{6, 8, 9}, {8, 3, 4}, {6, 3, 1}},
  {{5, 6, 6}, {6, 0, 2}, {5, 0, 5}}
}

showing three possible matches for this particular input. For longer  
lists, the number of matches can be rather large; there are about 1000  
possibilities for a list of 100 random triples and finding them all can  
take some time (over a second on my computer). If you have at most one  
matching instance in any given list, or only require the first matching  
instance to be returned, you might wish to substitute Replace for  
ReplaceList.




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