背包重量>最大尺寸

Question

I am currently having a query that results like this

A,B,C,D, E = item

numbers = weight

1. A 15
2. B 23
3. C 10
4. D 8

5. E 88

    use Algorithm::Bucketizer; my $b = Algorithm::Bucketizer->new( bucketsize => 30); for my $i (1..10) { $b->add_item($i, 30+$i); } for my $bucket ($b->buckets()) { for my $item ($bucket->items()) { print "Bucket ", $bucket->serial(), ": Item $item\\n"; } print "\\n"; } 

http://search.cpan.org/~mschilli/Algorithm-Bucketizer-0.13/Bucketizer.pm

Using this module I am applying the knapsack algorithm to try to distribute the weights of the items to buckets

my $bucketizer = Algorithm::Bucketizer->new(bucketsize => $size);

The problem is that when the weight is bigger that the size I am searching for that weight gets excluded.

Example:

bucketsize => 30

5. E 88 this will get excluded

Is there another algorithm that could possibly fix this situation? Or is there a way to modify this one to not exclude the weight that is bigger than the size?

Is is it possible to adjust it to work like this?

If weight > size then fill only a bucket with that weight

Answer 1

Just pass the bucket size instead of the actual size for any items over the bucket size.

use Algorithm::Bucketizer qw( );
use List::Util            qw( min );

my @items = ...;
my $bucket_size = 30;

my $bzer = Algorithm::Bucketizer->new( bucketsize => $bucket_size );
for my $i (0..$#items) {
    $bzer->add_item( $i => min($items[$i], $bucket_size) );
}

my @bucketed_items = map { [ $bucket->items() ] } $bzer->buckets();

Alternatively, since you know oversized values will take up an entire bucket, filter them out and add them back to the results.

use Algorithm::Bucketizer qw( );

my @items = ...;
my $bucket_size = 30;

my $bzer = Algorithm::Bucketizer->new( bucketsize => $bucket_size );
my @bucketed_items;
for my $i (0..$#items) {
    if ($items[$i] >= $bucket_size) {
        push @bucketed_items, [ $i ];
    } else {
        $bzer->add_item( $i => $items[$i] );
    }
}

push @bucketed_items, map { [ $bucket->items() ] } $bzer->buckets();

Answer 2

I don't see where you're stuck. You merely add a pre-processing step to the existing algorithm. You make a single pass over the weights. When you find one >= bucketsize , simply fill one bucket with that weight. Then remove that weight and the bucket from the problem set and continue as usual.

In your example above, you would start with

bucket[0] = 88
weights = [15, 23, 10, 8]

Continue with your usual solution, appending the 88-kg bucket after you return.