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Re: Fast way to select those elements from a list that are in another

  • To: mathgroup at smc.vnet.net
  • Subject: [mg86782] Re: Fast way to select those elements from a list that are in another
  • From: Szabolcs Horvát <szhorvat at gmail.com>
  • Date: Thu, 20 Mar 2008 05:50:12 -0500 (EST)
  • Organization: University of Bergen
  • References: <frt574$sj8$1@smc.vnet.net>

Andrew Moylan wrote:
> Two lists of integers:
> 
> {a, b} = Table[RandomInteger[10000, 1000], {2}];
> 
> Which elements from a are in b?
> 
> Select[a, MemberQ[b, #] &]; // Timing
>>> {0.351, Null}
> 
> It takes about 0.351 seconds (on my slow laptop). Specialised
> functions for related tasks, such as Intersection[a, b], are much
> faster:
> 
> Intersection[a, b]; // Timing
>>> {0., Null}
> 
> Using Intersection, here's a somewhat faster way to select those
> elements from a that are in b:
> 
> With[
>    {c = Intersection[a, b]},
>    Select[a, MemberQ[c, #] &]
>    ]; // Timing
>>> {0.09, Null}
> 
> Is there a better, faster way to do this?
> 

Hi Andrew,

You did not formulate the problem precisely.  There are two differences 
between c and d = Select[a, MemberQ[c, #] &.  One is that c is sorted, 
while d is not, and the other is that duplicates are removed from c. 
Which of these two are important?

If only one of the two is important then I can come up with much faster 
solutions, but if *both* are important then the problem becomes more 
difficult.


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