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From: Peter Pein on 10 Jun 2010 08:05
Am Wed, 2 Jun 2010 06:07:17 +0000 (UTC)
schrieb Andrzej Kozlowski <akoz(a)mimuw.edu.pl>:

> This method seems to be fairly quick:
>
> test[p_, a_] :==
> Position[Complement[a, {p}], {___, Sequence @@ p, ___}, 1, 1] !== {}
>
> DeleteCases[a, _?(test[#, a] &)]
>
> {{x1,x2,x3,x13,x18},{x1,x2,x7,x12,x15},{x1,x4,x5,x9,x16},{x1,x2,x7,x12,x14,x18},{x1,x4,x5,x9,x11,x17},{x1,x4,x6,x8,x10,x17}}
>
> Andrzej Kozlowski
>
>
really nice :-)

From: Peter Pein on 10 Jun 2010 08:07
The RotateRight in my solution is superflous but it leads to the same
result as in Andrzeij's answer:

For[i = 1, i <= Length[a], i++; a = RotateLeft[a],
If[MemberQ[Complement[First[a], #] & /@ Rest[a], {}],
a = Rest[a]]]; RotateRight@a

Peter

Am Tue, 1 Jun 2010 08:23:18 +0000 (UTC)
schrieb Robert Wright <mathematicauser1(a)yahoo.com>:

> I have a list 'a' in which there are 'sets', and I want to reduce the
> list so that repeated patterns are eliminated.
>
> Here is an example list:
>
> a = {{x1, x2}, {x1, x4}, {x2, x3}, {x4, x5}, {x4, x6}, {x2, x7}, {x7,
> x12}, {x3, x13}, {x13, x18}, {x6, x8}, {x5, x9}, {x9, x11}, {x9,
> x16}, {x8, x10}, {x12, x14}, {x12, x15}, {x10, x17}, {x11, x17},
> {x14, x18}, {x1, x2, x3}, {x1, x4, x5}, {x1, x4, x6}, {x1, x2, x7},
> {x4, x6, x8}, {x4, x5, x9}, {x2, x7, x12}, {x2, x3, x13}, {x7, x12,
> x14}, {x5, x9, x16}, {x9, x11, x17}, {x8, x10, x17}, {x12, x14, x18},
> {x1, x4, x6, x8}, {x1, x4, x5, x9}, {x1, x2, x7, x12}, {x1, x2, x3,
> x13}, {x4, x5, x9, x11}, {x4, x6, x8, x10}, {x2, x7, x12, x14}, {x7,
> x12, x14, x18}, {x1, x4, x5, x9, x11}, {x1, x4, x6, x8, x10}, {x1,
> x2, x7, x12, x14}, {x1, x2, x3, x13, x18}, {x1, x2, x7, x12, x15},
> {x1, x4, x5, x9, x16}, {x1, x2, x7, x12, x14, x18}, {x1, x4, x5, x9,
> x11, x17}, {x1, x4, x6, x8, x10, x17}}
>
>
>
> The idea is to start with the first element, in this case {x1, x2},
> and see if it appears at the start of a subsequent sublist. So for
> example, because it appears in {x1, x2, x7, x12, x15}, and
> elsewhere, we can delete it. The process should be repeated until we
> get to the fundamental lists which contain all the sublists. In this
> case, the result should be:
>
> {
> {x1, x2, x3, x13, x18},
> {x1, x2, x7, x12, x15},
> {x1, x4, x5, x9, x16},
> {x1, x2, x7, x12, x14, x18},
> {x1, x4, x5, x9, x11, x17},
> {x1, x4, x6, x8, x10, x17}
> }
>
> I have tried to use DeleteDuplicates and FixedPoint as shown below,
> but I end up with an empty list!!
>
>
> myDeleteDuplicates[allPaths_] :=
> Module[{duplicates},
> duplicates =
> DeleteDuplicates[ allPaths, (#2[[1 ;; Length[#1]]] === #1) &];
> Complement[allPaths, duplicates]
> ]
>
> FixedPoint[myDeleteDuplicates, a]
>
> Help appreciated
>
> Robert



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