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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