Re: programing: reduce list to cycle
- To: mathgroup at smc.vnet.net
- Subject: [mg8650] Re: programing: reduce list to cycle
- From: "Xah" <xah at best.com>
- Date: Fri, 12 Sep 1997 04:11:03 -0400
- Organization: smtp.best.com
- Sender: owner-wri-mathgroup at wolfram.com
This is the second summary of the problem shortest Cycle posted around
(1997/09).
Problem:
I want to reduce a list to its shortest cycle. For example, if
myList={3,1,0,3,3,1,0,3,3,1,0,3}, then the desired result should be
{3,1,0,3}. How to do it? myList are not always complete cycles, in such
case, the whole list should be returned.
(*A friend:*)
Clear[shortestCycle];
shortestCycle[lis_List] :=
With[{l = Length[lis]},
Take[lis, Do[If[Mod[l,i]===0 && MatchQ[Partition[lis,i],{(x_)..}],
Return[i]],{i,1,l}]]];
(*Will Self wself at viking.emcmt.edu*)
Clear[repe,shortestCycleWillS];
repe[x_List,n_Integer?Positive]:=Flatten[Table[x,{n}],1];
shortestCycleWillS[x_List]:=
Module[{m,f,temp},m=Length[x];f=(Divisors at m);
Do[If[repe[temp=Take[x,f[[k]] ],m/(f[[k]])]==x,Return[temp]],{k,1,
Length[f]}]];
(*Alan Hayes (hay at haystack.demon.co.uk)*)
(*a variant on the first one*)
Clear[shortestCycleAlanH];
shortestCycleAlanH[x_]:=
If[MatchQ[Partition[x, #],{u_
..}],Throw[Take[x,#]]]&/@Divisors[Length[x]]//
Catch
(*Wouter Meeussen <w.meeussen.vdmcc at vandemoortele.be>*)
Clear[shortestCycleWouter];
shortestCycleWouter[li_]:=
First@(Partition[li,#]&)@Module[{i=1},While[RotateRight[li,i]=!=li,i++];i]
(*Timing comparison*)
cycList=Table[Random[Integer,{1,9}],{i,1,5}]
niceCycle=Flatten at Table[cycList,{i,1,2000}];
notCycle=Flatten[{niceCycle,a}];
Length at Flatten@niceCycle
solutions={shortestCycle,shortestCycleAlanH,shortestCycleWillS,
shortestCycleWouter};
results=(Timing at #@niceCycle)&/@solutions;
{First at #,Equal@@Last at #}&@Transpose at results
{{0.433333 Second,0.416667 Second,0.333333 Second,0.15 Second},True}
results=(Timing at #@notCycle)&/@solutions;
{First at #,Equal@@Last at #}&@Transpose at results
{{1.83333 Second,0.35 Second,0.25 Second,285.683 Second},True}
(*Conclusion*)
Wouter's solution is the fastest by several orders if the input is a nice
cycle, otherwise it's several order slower. The overall fastest is Will's
solution. Still, we are missing a pure pattern-matching solution.
Xah
xah at best.com
http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html
Mountain View, CA, USA