``````# \$Id: Knapsack.pm,v 1.11 2004/10/23 18:52:19 alex Exp \$

package Algorithm::Knapsack;

use strict;
use vars qw(\$VERSION);

\$VERSION = '0.02';

Algorithm::Knapsack - brute-force algorithm for the knapsack problem

use Algorithm::Knapsack;

my \$knapsack = Algorithm::Knapsack->new(
capacity => \$capacity,
weights  => \@weights,
);

\$knapsack->compute();

foreach my \$solution (\$knapsack->solutions()) {
foreach my \$index (@{\$solution}) {
# do something with \$weights[\$index]
}
}

The knapsack problem asks, given a set of items of various weights, find a
subset or subsets of items such that their total weight is no larger than
some given capacity but as large as possible.

This module solves a special case of the 0-1 knapsack problem when the
value of each item is equal to its weight. Capacity and weights are
restricted to positive integers.

=over 7

=item B<new>

my \$knapsack = Algorithm::Knapsack->new(
capacity => \$capacity,
weights  => \@weights,
);

Creates a new Algorith::Knapsack object. Value of \$capacity is a
positive integer and \@weights is a reference to an array of positive
integers, each of which is less than \$capacity.

=cut

sub new {
my \$class = shift;
my \$self = {
capacity    => 0,       # total capacity of this knapsack
weights     => [],      # weights to be packed into the knapsack
@_,
solutions   => [],      # lol of indexes to weights
emptiness   => 0,       # capacity minus sum of weights in a solution
};
bless \$self, \$class;
}

=item B<compute>

\$knapsack->compute();

Iterates over all possible combinations of weights to solve the knapsack
problem. Note that the time to solve the problem grows exponentially with
respect to the number of items (weights) to choose from.

=cut

sub compute {
my \$self = shift;
\$self->{emptiness} = \$self->{capacity};
\$self->_knapsack(\$self->{capacity}, [0 .. \$#{ \$self->{weights} }], []);
}

sub _knapsack {
my \$self = shift;
my \$capacity = shift;
my @indexes  = @{ shift() };
my @knapsack = @{ shift() };

while (\$#indexes >= 0) {
my \$index = shift @indexes;
next if \$self->{weights}->[\$index] > \$capacity;

if (\$capacity - \$self->{weights}->[\$index] < \$self->{emptiness}) {
\$self->{emptiness} = \$capacity - \$self->{weights}->[\$index];
\$self->{solutions} = [];
}
if (\$capacity - \$self->{weights}->[\$index] == \$self->{emptiness}) {
push(@{ \$self->{solutions} }, [@knapsack, \$index]);
}

\$self->_knapsack(\$capacity - \$self->{weights}->[\$index],
\@indexes,
[@knapsack, \$index]);
}
}

=item B<solutions>

my @solutions = \$knapsack->solutions();

Returns a list of solutions. Each solution is a reference to an array of
indexes to @weights.

=cut

sub solutions {
my \$self = shift;
return @{ \$self->{solutions} };
}

1;

__END__

=back

The following program solves the knapsack problem for a list of weights
(14, 5, 2, 11, 3, 8) and capacity 30.

use Algorithm::Knapsack;
my @weights = (14, 5, 2, 11, 3, 8);
my \$knapsack = Algorithm::Knapsack->new(
capacity => 30,
weights  => \@weights,
);
\$knapsack->compute();
foreach my \$solution (\$knapsack->solutions()) {
print join(',', map { \$weights[\$_] } @{\$solution}), "\n";
}

The output from the above program is:

14,5,11
14,5,3,8
14,2,11,3