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MathGroup Archive 1999

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Re: Re: Fast List-Selection

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19940] Re: [mg19925] Re: [mg19880] Fast List-Selection
  • From: "Arnold Knopfmacher" <arnoldk at cam.wits.ac.za>
  • Date: Wed, 22 Sep 1999 04:11:19 -0400
  • Organization: MS, University of the Witwatersrand
  • Sender: owner-wri-mathgroup at wolfram.com

Some Timings for Andrzejs functions applied to the list

l=Table[Random[Integer,{0,9}],{100000}];

findsequence[3][l] // Timing
{3.51 Second,{{32432}}}

findsequence[4][l] // Timing
{2.58 Second,32432}

findsequence[5][l] // Timing
{5.27 Second,32432}

Carl Wolls function:

rep[ls_,n_]:=Position[Partition[ls,n,1],{x_ ..}]

rep[l,6]//Timing
{2.47 Second,{{32432}}}

Rob Pratts function

Consec[l_,n_]:=
  Flatten[Position[Partition[l,n,1],Table[x_,{n}]]]
 
Consec[l,6]//Timing
{2.14 Second,{32432}}

My function  is still faster (at least for this test list and under Mathematica 
3)

dif[s_]:=Drop[s,1]-Drop[s,-1];
nconsecB[s_,n_]:=
  Module[{ss=Flatten[Position[dif[s],0]],ans={}},
    Do[If[ss[[i+n-2]]-ss[[i]]==n-2,ans={ans,ss[[i]]}],{i,Length[ss]-n+2}];ans]

nconsecB[l,6]//Timing
{1.81 Second,{32432}}

Perhaps my function can be rewritten in a more elegant form?

Arnold Knopfmacher
Witwatersrand University
South Africa


> Date:          Tue, 21 Sep 1999 02:22:54 -0400
> Subject: [mg19940]       [mg19925] Re: [mg19880] Fast List-Selection
> From:          "Andrzej Kozlowski" <andrzej at tuins.ac.jp>
To: mathgroup at smc.vnet.net
> To:            mathgroup at smc.vnet.net

> I have managed to produce four additional examples, three  of which seem to
> be faster than yours. I will change the search to 6 rather than 7
> consecutive identical elements because I want to use for my testing a famous
> example:
> 
> In[1]:=
> l = RealDigits[N[Pi, 10000]][[1]];
> 
> Hear are the functions I will test, beginning with yours:
> 
> In[2]:=
> findsequence[1][l_] := Do[If[Count[t = Take[l, {i, i + 5}], t[[1]]] == 6,
> Print[i]], {i, 1, Length[l] - 5}]
> 
> In[3]:=
> findsequence[2][l_] :=
>   Position[l /. {a___, y_, y_, y_, y_, y_, y_, b___} -> {a, mark, b}, mark,
> 1]
> 
> In[4]:=
> findsequence[3][l_] :=
>   Module[{m = Split[l], mark},
>     Position[Flatten[m /. Cases[m, _?(Length[#] == 6 &)][[1]] -> mark],
> mark,
>       1]]
> 
> In[5]:=
> findsequence[4][l_] :=
>   Module[{m = Split[l]},
>     Length[Flatten[
>           Take[m, Position[m, Select[m, Length[#] == 6 &][[1]]][[1, 1]] -
>               1]]] + 1]
> 
> In[6]:=
> f[x_, x_, x_, x_, x_, x_] := 0;
> f[y__] := 1;
> g[l_, i_] := f[Apply[Sequence, Take[l, {i, i + 5}]]];
> findsequence[5][l_] := Scan[If[g[l, #] == 0, Return[#]] &,
> Range[Length[l]]];
> 
> Now the test:
> 
> In[9]:=
> Table[findsequence[i][l] // Timing, {i, 1, 5}]
> 763
> Out[9]=
> {{1.38333 Second,
>     Null}, {2.18333 Second, {{763}}}, {0.783333 Second, {{763}}}, {0.683333
> Second, 763}, {0.183333 Second, 763}}
> 
> The last one wins by a big margin The programs using Split may do better on
> other machines (I am using Mac PowerBook G3 ,233 mghz) because there seems
> to be something wrong with Split on the Mac where it doesn't scale linearly
> with the size of the input.
> 
> Finally: In[10]:=
> Take[l, {763, 763 + 5}]
> Out[10]=
> {9, 9, 9, 9, 9, 9}
> --
> Andrzej Kozlowski
> Toyama International University
> JAPAN
> http://sigma.tuins.ac.jp
> http://eri2.tuins.ac.jp
> 
> 
> ----------
> >From: Hans Havermann <haver at total.net>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> >To: mathgroup at smc.vnet.net
> >Subject: [mg19940] [mg19925] [mg19880] Fast List-Selection
> >Date: Mon, Sep 20, 1999, 7:47 AM
> >
> 
> > I have a list 's' composed of a large number of (small) integers. I wish to
> > search this list for instances of 7 consecutive, identical elements.
> >
> > My approach is:
> >
> > Do[If[Count[t = Take[s, {i, i + 6}], t[[1]]] == 7,
> >     Print[i]], {i, 1, Length[s] - 6}]
> >
> > Can anyone think of a *faster* way of doing this?
> >
> >
> >
> 
> --
> Andrzej Kozlowski
> Toyama International University
> JAPAN
> http://sigma.tuins.ac.jp
> http://eri2.tuins.ac.jp
> 
> 
> ----------
> >From: Hans Havermann <haver at total.net>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> >To: mathgroup at smc.vnet.net
> >Subject: [mg19940] [mg19925] [mg19880] Fast List-Selection
> >Date: Sun, 19 Sep 1999 18:47:32 -0400
> >
> 
> > I have a list 's' composed of a large number of (small) integers. I wish to
> > search this list for instances of 7 consecutive, identical elements.
> >
> > My approach is:
> >
> > Do[If[Count[t = Take[s, {i, i + 6}], t[[1]]] == 7,
> >     Print[i]], {i, 1, Length[s] - 6}]
> >
> > Can anyone think of a *faster* way of doing this?
> >
> >
> > 
> 
> 


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