Expanding Round-robin tournament 1v1 to a 1v1v1v1

Question

I am trying to expand and improve the round-robin algorithm from 1v1 group to a 1v1v1v1 group(something like free for all). I've made the function itself to do the schedule, but when I tried to expand it, some teams repetead. For example, I have 16 teams and I want to have 5 rounds, team 1 appears 7 times in 5 rounds and team2 appears 3 times in 5 rounds. I need them to appear 5 times at most.I really can't understand how I can do it. Any advice is welcomed and links.

function make_schedule(array $teams, int $rounds = null, bool $shuffle = true, int $seed = null): array
{


    $teamCount = count($teams);


   if($teamCount < 4) {
        return [];
    }
    //Account for odd number of teams by adding a bye
    if($teamCount % 2 === 1) {
        array_push($teams, null);
        $teamCount += 1;
    }
    if($shuffle) {
        //Seed shuffle with random_int for better randomness if seed is null
        srand($seed ?? random_int(PHP_INT_MIN, PHP_INT_MAX));
        shuffle($teams);
    } elseif(!is_null($seed)) {
        //Generate friendly notice that seed is set but shuffle is set to false
        trigger_error('Seed parameter has no effect when shuffle parameter is set to false');
    }
    $quadTeamCount = $teamCount / 4;
    if($rounds === null) {
        $rounds = $teamCount - 1;
    }

    $schedule = [];

    for($round = 1; $round <= $rounds; $round += 1) {
        $matchupPrev = null;

        foreach($teams as $key => $team) {
            if($key >= $quadTeamCount ) {
                break;
            }

            $keyCount = $key + $quadTeamCount;
            $keyCount2 = $key + $quadTeamCount + 1;
            $keyCount3 = $key + $quadTeamCount + 2;


            $team1 = $team;
            $team2 = $teams[$keyCount];
            $team3 = $teams[$keyCount2];
            $team4 = $teams[$keyCount3];


            //echo "<pre>Round #{$round}: {$team1} - {$team2} - {$team3} - {$team4} == KeyCount: {$keyCount} == KeyCount2: {$keyCount2} == KeyCount3: {$keyCount3}</pre>";

            //Home-away swapping
            $matchup = $round % 2 === 0 ? [$team1, $team2, $team3, $team4 ] : [$team2, $team1, $team4, $team3];

            $schedule[$round][] = $matchup ;
        }
        rotate($teams);
    }

    return $schedule;
}

Rotate function:

   function rotate(array &$items)
{
    $itemCount = count($items);
    if($itemCount < 3) {
        return;
    }
    $lastIndex = $itemCount - 1;
    /**
     * Though not technically part of the round-robin algorithm, odd-even 
     * factor differentiation included to have intuitive behavior for arrays 
     * with an odd number of elements
     */
    $factor = (int) ($itemCount % 2 === 0 ? $itemCount / 2 : ($itemCount / 2) + 1);
    $topRightIndex = $factor - 1;
    $topRightItem = $items[$topRightIndex];
    $bottomLeftIndex = $factor;
    $bottomLeftItem = $items[$bottomLeftIndex];
    for($i = $topRightIndex; $i > 0; $i -= 1) {
        $items[$i] = $items[$i - 1];
    }
    for($i = $bottomLeftIndex; $i < $lastIndex; $i += 1) {
        $items[$i] = $items[$i + 1];
    }
    $items[1] = $bottomLeftItem;
    $items[$lastIndex] = $topRightItem;
}

For example:

If I set rounds to 5, every team play 5 matches. Array example Screenshot

Dealing with the 5th round:

Well, after I thought for a bit, maybe there isn't a way for them to play without repeatence, but if it is lowered to minumum, like every team should play 5 times only - this means once a round. That's what I meant. And what I meant under 'they repeat' is that there are like: 16 teams, 5 rounds and some teams are going like 7 times for all these rounds and other teams are going 3 times for these 5 rounds. I want to avoid this and to make every team play 5 rounds at most.

Answer 1

Your foreach() with the selection of the other 3 teams is wrong. One of them have to make steps with a multiple of 4. If you don't, you will select the teams at the beginning more than one and don't select the teams at the end of the array at all. This will result in wrong team matchups like this (teams are letters here):

abcd
bcde
cdef
defg

And then your break; hits.

Instead it should look something like this:

for ($i=0; $i<4; $i++) {
    $matchup = array();
    for ($j=0; $j<4; $j++) {
        $matchup[] = $teams[4*$i+$j];
    }
    $schedule[$round][] = $matchup ;
}

This way you get the following pairing (again, using letters as teams):

abcd
efgh
ijkl
mnop

This algorithm will split the team list in four groups:

abcd|efgh|ijkl|mnop

Keep in mind that depending on the shuffling of the $teams array for the next round you might get the same opponent twice.

adei|klnf|gjmc|pobh

Here the teams ad, kl and op will face again.