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Two dimensional sets intersection

by menth0l (Monk)
on Apr 10, 2013 at 13:12 UTC ( #1027966=perlquestion: print w/ replies, xml ) Need Help??
menth0l has asked for the wisdom of the Perl Monks concerning the following question:

Hi

I have two discontinuous sets of values and some pairs from each sets are "valid" and have assigned values, for example:
# subset 1 of (A..Z) set_1 = (A, B, C, X, Y, Z) # subset 2 of (a..z) set_2 = (q, w, r, t, u) # valid pairs valid = ((A,q) = 1, (A,u) = 6, (A,k) => 3, (C,t) = 10, (Z,u) = 30)
I have a problem with "translating" this to perl. I know I need some kind of map for storing information about valid pairs and their id (like python's map of tuples: (x,y) => z). But having two sets, each consisting of 100 elements requires 100x100=10000 combinations... Is there any quicker method for this?

If I'd have an index like this:
my %INDEX = { A => { q => 1, u => 6, k => 3 }, C => { t => 10 }, Z => { u => 30 }, M => { q => 100 } }
I could narrow search by creating intersection (e.g. using Set::Object):
# narrow by first set (set_1) x (keys %INDEX) = (set_1) x (A, C, M, Z) = (A, C, Z)
then i would be left with an array of hash-refs and do:
set_2 x (q, u, k) + set_2 x (t) + set_2 x (u) = (1, 6, 10, 30)

I don't like this idea though and I don't know if it would be faster than combinations hash checks. Is there a perl module that would help me with this?

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Re: Two dimensional sets intersection
by daxim (Chaplain) on Apr 10, 2013 at 13:28 UTC
    This is a FAQ.
    use Hash::MultiKey; tie my %valid, 'Hash::MultiKey'; %valid = ( [qw(A q)] => 1, [qw(A u)] => 6, [qw(A k)] => 3, [qw(C t)] => 10, [qw(Z u)] => 30, );
Re: Two dimensional sets intersection
by LanX (Canon) on Apr 10, 2013 at 14:29 UTC
    first of all I have to say that I have the impression that you are trying to reinvent a wheel from graph theory.

    Your structure looks for me like a weighted bipartite graph, and you are trying to find a subgraph.

    Did you check CPAN for related modules?

    > (like python's map of tuples: (x,y) => z)

    don't know enough about Python, but this can easily be simulated in Perl with old-style multidim hashes and grepping with a split on the keys.

    DB<116> $index{"A","a"}=1 => 1 DB<117> $index{"A","b"}=2 => 2 DB<118> $index{"B","a"}=3 => 3 DB<119> $index{"B","b"}=4 => 4 DB<120> grep { my ($k1,$k2) = split /$;/,$_; $k1 eq "A" } keys %inde +x => ("A\34a", "A\34b") DB<121> %set1=(A=>1) => ("A", 1) DB<122> %set2=(a=>1) => ("a", 2) DB<124> grep { my ($k1,$k2) = split /$;/,$_; $set1{$k1} and $set2{$k +2} } keys %index => "A\34a"

    This brute force search might be elegantš, but for sure not as efficient as looping thru your hierarchical structure.

    Cheers Rolf

    ( addicted to the Perl Programming Language)

    1) especially when delegating the split to a function called by grep

    grep &splitted(\%set1,\%set2) , keys %index

    update

    added missing keys

Re: Two dimensional sets intersection
by Not_a_Number (Parson) on Apr 10, 2013 at 20:44 UTC

    No need to worry about narrowing your search or whatever. Hash lookups are fast.

    The code below creates a hash for a 100 x 100 matrix. It also assumes that each matrix pair has a value (worst case, given your 'spec'). To simplify validation, I make this value 1, but changing it to any other number makes no difference to the time required for lookup.

    Subsequently, I make another worst-case assumption, namely that your lists of search terms (what you call Subset 1 and Subset 2) are maximally large.

    On my machine, it finishes before I can blink. Run it and see:

    use strict; use warnings; # Create 100 x 100 datastructure: my @uc = ( 'AA' .. 'DV' ); my @lc = ( 'aa' .. 'dv' ); my %index; for my $k ( @uc ) { for my $v ( @lc ) { $index{$k}{$v} = 1; } } # Parse it: my $score; for my $k ( @uc ) { # or: for my $k ( @subset_1 ) for my $v ( @lc ) { # or: for my $v ( @subset_2 ) $score += $index{$k}{$v} || 0; } } print $score;

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