Re: Select from list

• To: mathgroup at smc.vnet.net
• Subject: [mg87777] Re: Select from list
• From: thomas <thomas.muench at gmail.com>
• Date: Wed, 16 Apr 2008 22:32:08 -0400 (EDT)
• References: <fu4fjb\$nhp\$1@smc.vnet.net>

```On Apr 16, 11:06 am, Steve Gray <stev... at roadrunner.com> wrote:
> I have a list like this:
>
> ptX=
> {{1, 2, 3, 4}, {1, 2, 3, 5}, {1, 2, 4, 5}, {1, 3, 4, 5}, {2, 3, 4, 5}}
>
> and I want a list pointing to all the sublists above that contain both
> a 2 and a 3. In this example I would get {1,2,5}. The best solution I
> have, with more generality, is:
>
> va = 2;
> vb = 3;
> za = Map[Cases[#1, va]&, ptX] /. {} -> {0}
> zb = Map[Cases[#1, vb]&, ptX] /. {} -> {0}
> Flatten[Position[za*zb, {va*vb}]]
>
> which gives
>
> {{2}, {2}, {2}, {0}, {2}}
> {{3}, {3}, {0}, {3}, {3}}
> {1, 2, 5}.
>
> (This doesn't work if va or vb is zero. That's ok.)
> There's probably a better way. Anyone? Thank you.
>
> Steve Gray

Hi Steve,

This approach is using a trick from Carl Woll to get non-zero
positions in a list:

NonzeroPositions[data_] :=
SparseArray[data] /. SparseArray[_, _, _, x_] :> Flatten[x[[2, 2]]]

With that:

findTwo[ptX_,va_,vb_]:=
NonzeroPositions[Total[-Unitize[ptX - va] + 1, {2}]*Total[-Unitize[ptX
- vb] + 1, {2}]]

Here,
-Unitize[ptX - va] + 1
replaces each occurance of va with 1, others are 0.

Total[...,{2}] then adds up the values (i.e. you get 0 if va is not
there)

With

list = Table[RandomSample[Range[9], 4], {10^6}];

We get

In[10]:= Timing[findTwo[list, 2, 3] ;][[1]]
Out[10]= 0.641

and some other approaches:
In[11]:= Timing[
Flatten[Position[(Map[Cases[#1, 2] &, list] /. {} -> {0})*(Map[
Cases[#1, 3] &, list] /. {} -> {0}), {2*3}]];][[1]]
Out[11]= 12.063

```

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