comment on

blokhead's (now-stricken) array above looked awfully like a Latin square to me, and in my search for a Latin square-generating algorithm, I came across Latin Squares, which describes the technique when applied to round-robin scheduling.

Summary follows the readmore

Only works for EVEN N. For odd N, add 1 and treat the extra player as a bye.

Essentially, you start (step 1:) with an addition chart, mod N-1.

+  0 1 2 3 4 5 6

0  0 1 2 3 4 5 6
1  1 2 3 4 5 6 0
2  2 3 4 5 6 0 1
3  3 4 5 6 0 1 2
4  4 5 6 0 1 2 3
5  5 6 0 1 2 3 4
6  6 0 1 2 3 4 5
[download]

(Step 2:) Copy the diagonal entries to the ends of their columns and the ends of their rows (creating an NxN array)

+  0  1  2  3  4  5  6

0 *0* 1  2  3  4  5  6  0
1  1 *2* 3  4  5  6  0  2
2  2  3 *4* 5  6  0  1  4
3  3  4  5 *6* 0  1  2  6
4  4  5  6  0 *1* 2  3  1
5  5  6  0  1  2 *3* 4  3
6  6  0  1  2  3  4 *5* 5
7  0  2  4  6  1  3  5
[download]

(Step 3:) Relabel the 0's as N-1's, relabel the player numbers, and delete the diagonal.

P  1 2 3 4 5 6 7 8

1    1 2 3 4 5 6 7
2  1   3 4 5 6 7 2
3  2 3   5 6 7 1 4
4  3 4 5   7 1 2 6
5  4 5 6 7   2 3 1
6  5 6 7 1 2   4 3
7  6 7 1 2 3 4   5
8  7 2 4 6 1 3 5
[download]

Update: To bring this back to perl-land:
plays_in_round(player1, player2, N) returns the round, in a tournament of N players, in which player1 plays player2
ex: plays_in_round(5,7,8) == 3

sub plays_in_round {
    my ($p1, $p2, $n) = @_;
    $n++ if $n % 2;
    return undef if $p1 == $p2;
    ($p1, $p2) = ($p2, $p1) if $p1 > $p2;
    $p2 = $p1 if $p2 == $n;
    my $r = $p1 + $p2 - 2;
    $r %= $n - 1;
    $r || ($n - 1);
}
[download]

In reply to Re: Round robin tournament problem by benizi
in thread Round robin tournament problem by CiceroLove

Are you posting in the right place? Check out Where do I post X? to know for sure.
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big> <blockquote> <br /> <dd> <dl> <dt> <em> <font> <h1> <h2> <h3> <h4> <h5> <h6> <hr /> <i> <li> <nbsp> <ol> <p> <small> <strike> <strong> <sub> <sup> <table> <td> <th> <tr> <tt> <u> <ul>
Snippets of code should be wrapped in <code> tags not <pre> tags. In fact, <pre> tags should generally be avoided. If they must be used, extreme care should be taken to ensure that their contents do not have long lines (<70 chars), in order to prevent horizontal scrolling (and possible janitor intervention).
Want more info? How to link or How to display code and escape characters are good places to start.


Syntactic Confectionery Delight
	PerlMonks