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I have 13 soccer teams who plays 2 games by week (10 weeks in total). Since I have an odd number of teams, I add a fictive team called "Practice". Also, I would like to generate a schedule in which each team plays against the other teams only once. I know the list of those games are obtained by C(14, 2) = 91 couples of games.

However, my biggest problem is to sort them in a way that satisfy my constraints : Each one plays against each one.

Since I have 10 weeks and each week is 2 games, it gives a total of 20 games for each teams (20 * 14 / 2), thus a big total of 140 games to schedule. Since I have a 91-games block, I just want to repeat it to complete to 140 games.

I tried many code around here and each time I got the same problem that a Team A plays a Team B in week 1 and then plays again each other on Week 3 which is not correct.

I am pretty sure there's a solution to this (backtracking or graph theory), but I didn't find it at the moment.

Thanks to all for your time :)

Provost
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  • Are there any other constraints? Normally you have some additional constraints like forced home-match for A on date X...). And what about the desired *randomness*. I think it's possible to create a table by **construction** (linear or quadratic time), but in this case there would be some kind of structure like A vs. Z, B vs. Y, ... (looks not random; should be simple to do with this double-round-robin scheme). There is an even harder version of this known as tournament-schedule problem. Most of the time you would use Mixed-integer programming or Constraint-programming for problems like these! – sascha Jun 02 '16 at 21:14
  • No, there's no constraint since I want all the teams plays against each other one. Those teams are for young players (4-7 years old) and they all play at the same facility so we don't need return games. – Provost Jun 02 '16 at 21:48

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