How to match up pairs in a round robin tournament?

Andrej Mrzi'me

I'm making a tournament app where a number of (4, 6, or 8) players would be matched up against each other.

It is round based. So if there are for example 6 players in total, there would be 5 rounds with 3 pairs each. Every player can show up only once per round.

What I tried

I've been using for-loops to get the combinations needed, but how can I separate the pairs into rounds such that they don't repeat? Here is what I have done so far (making every combination):

<?php
$players = [1,2,3,4,5,6];

for($i = 0; $i < count($players); $i++):
    for($j = 0; $j < $i; $j++):
         $pair1 = $players[$j];
         $pair2 = $players[$i];
         $pairs[] = $pair1.$pair2;          
    endfor;
endfor;
/* Output:
   [
     0 => "12"
     1 => "13"
     2 => "23"
     3 => "14"
     4 => "24"
     5 => "34"
     6 => "15"
     7 => "25"
     8 => "35"
     9 => "45"
     10 => "16"
     11 => "26"
     12 => "36"
     13 => "46"
     14 => "56"
   ]*/

My question

Is there any generic way to distribute the pairs into rounds, without players showing up more than once in the same round?

Example

1^st round: 12, 34, 56;
2^nd round: 13, 25, 46...

trincot

You could use this code. It is based on the scheduling algorithm for round robin:

$players = [1,2,3,4,5,6];

$n = count($players);
for ($r = 0; $r < $n - 1; $r++) {
    for ($i = 0; $i < $n / 2; $i++) {
        $rounds[$r][] = [$players[$i], $players[$n-1 - $i]];
    }
    // Perform round-robin shift, keeping first player in its spot:
    $players[] = array_splice($players, 1, 1)[0];
}
// shift once more to put array in its original sequence:
$players[] = array_splice($players, 1, 1)[0];

Note that this puts the pairs into sub-arrays. It is not a good idea to concatenate them as strings, as this will just make it harder to extract the individual numbers from them again.

After the above code has run, the array $rounds is:

[
  [[1,6],[2,5],[3,4]]
  [[1,2],[3,6],[4,5]]
  [[1,3],[4,2],[5,6]]
  [[1,4],[5,3],[6,2]]
  [[1,5],[6,4],[2,3]]
]

The round-robin shift that happens in the loop, can be visualised like this, where the array is "folded" half-way to also show who is paired with who (in columns):

Player 1 never moves, the player at place 2 is sliced out of the array, and pushed on the end of the array, which means it will arrive in place 6.

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edited at2020-10-25

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