Generating Fixture Lists

Update 2007-03-21: If all you want to do is generate a fixtures list you can use my Fixtures Generator

I’ve been trying to find out how to generate fixture lists for some time (it is harder than it sounds!) and I finally worked it out thanks to this page about a fixture generating algorithm. My Java implementation of the algorithm is below.

/* 
 * This code owes an enormous debt to 
 * http://www.barrychessclub.org.uk/berger2001.htm 
 */

import java.util.Arrays;

public class Fixtures2 {

    public static void main(String[] args) {
        
        // Find out how many teams we want fixtures for.
        int teams = 0;
        try {
            teams = Integer.parseInt(args[0]);
        } catch (NumberFormatException e) {
            System.err.println("Please state number of teams as first arg.");
            System.exit(0);
        }
        
        // If odd number of teams add a "ghost".
        boolean ghost = false;
        if (teams % 2 == 1) {
            teams++;
            ghost = true;
        }
        
        // Generate the fixtures using the cyclic algorithm.
        int totalRounds = teams - 1;
        int matchesPerRound = teams / 2;
        String[][] rounds = new String[totalRounds][matchesPerRound];
        
        for (int round = 0; round < totalRounds; round++) {
            for (int match = 0; match < matchesPerRound; match++) {
                int home = (round + match) % (teams - 1);
                int away = (teams - 1 - match + round) % (teams - 1);
                // Last team stays in the same place while the others
                // rotate around it.
                if (match == 0) {
                    away = teams - 1;
                }
                // Add one so teams are number 1 to teams not 0 to teams - 1
                // upon display.
                rounds[round][match] = (home + 1) + " v " + (away + 1);
            }
        }
        
        // Interleave so that home and away games are fairly evenly dispersed.
        String[][] interleaved = new String[totalRounds][matchesPerRound];
        
        int evn = 0;
        int odd = (teams / 2);
        for (int i = 0; i < rounds.length; i++) {
            if (i % 2 == 0) {
                interleaved[i] = rounds[evn++];
            } else {
                interleaved[i] = rounds[odd++];
            }
        }
        
        rounds = interleaved;

        // Last team can't be away for every game so flip them
        // to home on odd rounds.
        for (int round = 0; round < rounds.length; round++) {
            if (round % 2 == 1) {
                rounds[round][0] = flip(rounds[round][0]);
            }
        }
        
        // Display the fixtures        
        for (int i = 0; i < rounds.length; i++) {
            System.out.println("Round " + (i + 1));
            System.out.println(Arrays.asList(rounds[i]));
            System.out.println();
        }
        
        System.out.println();
        
        if (ghost) {
            System.out.println("Matches against team " + teams + " are byes.");
        }
        
        System.out.println("Use mirror image of these rounds for "
            + "return fixtures.");
    }

    private static String flip(String match) {
        String[] components = match.split(" v ");
        return components[1] + " v " + components[0];
    }
}

Update 2005-06-05: Now allows “complementary teams”, that is – teams that never play at home at the same time as each other. For example, try 10 teams — for each pair from 1 & 6, 2 & 7, 3 & 8, 4 & 9, and 5 & 10, both are never both at home. It was meant to be in the original program but a bug in my code was fouling things up.

Update 2007-03-21: You might also want to see the source code to my PHP fixtures generator