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### Re^2: Groups of Objects with Common Attributes

by vr (Curate)
 on May 17, 2018 at 17:22 UTC Need Help??

After couple days of looking up what on earth is clustering, k-means, etc. -- hopeless -- I took closer look at your code. Wow, so simple. Thanks, martink! Here is re-factored version, if I may, discarding all that was perceived superfluous and simplifying (to fit my brain). So it's, effectively, just 2 plain loops: over all attributes and all items. Loop over items doesn't add to example with pumpkins, but is required for other test cases.

I wonder, is it a mathematical fact, that even for 500 items and 75 attributes, there can be no more than 575 sets of common attributes? It somewhat contradicts to what I remember from combinatorics.

```use strict;
use warnings;
use feature 'say';
use List::Util qw/ uniq all /;
use Data::Dump 'dd';

my \$item2attr = {
apple   => { red    => 1, round => 1, plant => 1, fruit     => 1 }
+,
orange  => { orange => 1, round => 1, plant => 1, fruit     => 1 }
+,
pumpkin => { orange => 1, round => 1, plant => 1, vegetable => 1 }
+,
ball    => { red    => 1, round => 1, toy   => 1 },
};

# list of all items and attributes
my @items = sort keys %\$item2attr;
my @attr  = sort( uniq( map { keys %\$_ } values %\$item2attr ));

# flip the hash
my \$attr2item;
for my \$attr ( @attr ) {
for ( @items ) {
\$attr2item-> { \$attr }{ \$_ } = 1
if \$item2attr-> { \$_ }{ \$attr }
}
}

#dd \$item2attr;
#say '-----------------------------------';
#dd \$attr2item;
#say '-----------------------------------';

my %solutions;      # hash, to prevent duplicates

for ( @attr ) {
my @items_ = keys %{ \$attr2item-> { \$_ }};

my @attr_ = grep {
my \$attr = \$_;
all { \$item2attr-> { \$_ }{ \$attr }} @items_
} @attr;

}

for ( @items ) {
my @attr_ = keys %{ \$item2attr-> { \$_ }};

my @items_ = grep {
my \$item = \$_;
all { \$attr2item-> { \$_ }{ \$item }} @attr_
} @items;

}

dd values %solutions;

# then filter solutions for required number of common
# attributes, or find max set of common attributes,
# or find max set of items with any common attributes, etc.

sub _add_solution {             # writes to %solutions
my ( \$attr, \$items ) = @_;

return unless \$#\$items;     # skip uninteresting
@\$_ = sort @\$_ for @_;

\$solutions{ join ',', @\$attr } = [
scalar @\$attr,          # count of attributes
scalar @\$items,         # count of items
\$attr,                  # attribute list
\$items                  # item list
]
}

__END__

(
[2, 2, ["red", "round"], ["apple", "ball"]],
[2, 3, ["plant", "round"], ["apple", "orange", "pumpkin"]],
[1, 4, ["round"], ["apple", "ball", "orange", "pumpkin"]],
[3, 2, ["fruit", "plant", "round"], ["apple", "orange"]],
[3, 2, ["orange", "plant", "round"], ["orange", "pumpkin"]],
)

Edit: fixed issue with sorting.

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