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Re: Round robin tournament problem

by blokhead (Monsignor)
on Oct 22, 2003 at 00:17 UTC ( #301122=note: print w/replies, xml ) Need Help??

in reply to Round robin tournament problem

Update 2: The first half of this post was found to be wrong, and lived inside <strike> tags for a long time. Now it's in HTML comments..
Update 2: Wouldn't you know it, in combinatorics class today we actually discussed this exact problem. It has an analogous problem in graph theory dealing with edge-colorings of complete graphs. In any case, the solution is certainly not NP-complete, and the algorithm is very simple with a visual explanation..

Make a circle out of the competitors, except put one player in the middle. For each round, match up the middle guy with someone, then match up the other ones in a symmetric. It's easier to understand what I mean by "symmetric" with a picture, so here's an example with n=8:

Round 1: match 8 with 1, then pair up the rest symmetric to that line.. 1 | 7---|----2 8 6----------3 5----4 Round 2: match 8 with 2, then pair up the rest symmetric to the line.. 1 7 \ 2 \ \^ \ 8^ \ 6 \ 3 \ \ \ \ 5 4 Round X: ... keep rotating around the circle, etc
You obviously never get duplicates with the person you put in the middle. But you will also never get duplicates with the other people in the circle, because there are an odd number of them to pair up. You won't get duplicates until you've rotated all the way around.

Doing this in code is pretty easy:

my @players = qw/Frodo Sam Merry Pippin Strider Gandalf Legolas Gimli/ +; ######## my $num = @players; die "must have even number of players" if $num % 2; for my $partner (0 .. $num-2) { print "Round #" . ($partner + 1) . ":\n"; print " $players[-1] vs $players[$partner]\n"; for my $pair (1 .. ($num-2)/2) { my $p1 = ($partner - $pair) % ($num - 1); my $p2 = ($partner + $pair) % ($num - 1); print " $players[$p1] vs $players[$p2]\n"; } }
Yay combinatorics class!


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[james28909]: Good morning!
[james28909]: I have a problem I am trying to solve. I am packaging scripts using pdk and would like the verify the executable name each time it is executed
[Corion]: Hi James!
[james28909]: I looked through the docs, and see that PerlApp::exe() is suppose to return this information but whenever i try to use this, i get the error "Undefined subroutine &PerlApp::exe called"
[james28909]: i just want to verify the integrity of the executables name each time it is run.
[Corion]: Weird. this documentation says what you say.
[Corion]: I assume you are experiencing this with your packaged program. Maybe also include in the packaging list?
[james28909]: has anyone else run into this problem? i have tried searching but have not returned many results

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