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=encoding UTF-8

=head1 NAME

Algorithm::Pair::Best2 - select pairings (designed for Go tournaments, but can be used for anything).

=head1 VERSION

version 2.040

=head1 SYNOPSIS

    use Algorithm::Pair::Best2;

    my $pair = Algorithm::Pair::Best2->new( [ options ] );

    $pair->add( item, [ item, ... ] );

    @new_pairs = $pair->pick( [ window ] );

=head1 DESCRIPTION

This is a re-write of Algorithm::Pair::Best.  The interface is simplified
and the implementation is significantly streamlined.

After creating an Algorithm::Pair::Best2 object (with -E<gt>B<new>), B<add>
items to the list of items (i.e: players) to be paired.  The final list
must contain an even number of items or B<pick>ing the pairs will throw an
exception.

Algorithm::Pair::Best2-E<gt>B<pick> explores all combinations of items and
returns the pairing list with the best (lowest) score.  This can be an
expensive proposition - the number of combinations goes up very fast with
respect to the number of items:

    items combinations
      2         1       (1)
      4         3       (1 * 3)
      6        15       (1 * 3 * 5)
      8       105       (1 * 3 * 5 * 7)
     10       945       (1 * 3 * 5 * 7 * 9
     12     10395       (1 * 3 * 5 * 7 * 9 * 11)
     14    135135       (1 * 3 * 5 * 7 * 9 * 11 * 13)

It is clearly unreasonable to try to pair a significant number of items.
Trying to completely pair even 30 items would take too long.

Fortunately, there is a way to get pretty good results for big lists,
even if they're not perfect.  Instead of trying to pair the whole list
at once, Algorithm::Pair::Best2 pairs a series of smaller groups in a
sliding window to get good 'local' results.

The B<-E<gt>new> method accepts a B<window> option to limit the number
of pairs in the sliding window.  The B<window> option can also be
overridden by calling B<pick> with an explicit window argument:

    $pair->pick($window);

The list should be at least partially sorted so that reasonable
pairing candidates are within the 'sliding window' of each other.
Otherwise the final results may not be globally 'best', but only
locally good.  For (e.g.) a tournament, sorting by rank is sufficient.

Here's how a window value of 5 works:  the best list for items 1
through 10 (5 pairs) is found.  Save the pairing for the top two items
and then slide the window down to pair items 2 through 12.  Save the
top pairing from this result and slide down again to items 4 through
14.  Keep sliding the window down until we reach the last 10 items
(which are completed in one iteration).  In this way, a large number
of pairings can be completed without taking factorial time.

=head1 METHODS

=over

=item my $pair = B<Algorithm::Pair::Best2-E<gt>new>( options )

Creates a B<new> Algorithm::Pair::Best2 object.

=item $pair-E<gt>B<add> ( item, [ item, ...] )

Add an item (or several items) to be paired.  Item(s) can be any scalar
or reference.  They will be passed (a pair at a time) to the B<scoreSub>
callback.

=item @new_pairs = $pair-E<gt>B<pick> ( ?$window? )

Returns the best pairing found using the sliding window technique as
discussed in DESCRIPTION above.  B<window> is the number of pairs in the
sliding window.  If no B<window> argument is passed, the B<window> selected
in the B<new>, or the default value is used.

B<pick> returns the list (or a reference to the list in scalar context) of
items in pairing order: new_pair[0] is paired to new_pair[1], new_pair[2]
to new_pair[3], etc.

If the number of items in the list (from B<add>) is not even, an exception
is thrown.

=back

=head1 OPTIONS

The B<-E<gt>new> method accepts the following options:

=over 4

=item B<window> => number of pairs

Sets the default number of pairs in the sliding window during B<pick>.  Can
also be set by passing a B<window> argument to B<pick>.

Default: 5

=item B<scoreSub> => reference to scoring callback

The callback is called as B<scoreSub>(item_0, item_1), where item_0 and item_1
are members of the list created by B<add>ing items.  The callback must
return a positive number representing the 'badness' of this pairing.  A
good pairing should have a number closer to 0 than a worse pairing.  If
B<scoreSub> returns a negative number, an exception is thrown.