如何在循环赛中配对? [英] How to match up pairs in a round robin tournament?

问题描述

我正在制作一个锦标赛应用程序，其中将有4名，6名或8名玩家相互竞争.

这是基于回合的.因此，例如，如果总共有6个玩家，那么将有5个回合，每个回合3对.每个玩家每回合只能出现一次.

我尝试过的

我一直在使用for循环来获取所需的组合，但是如何将这些对分成几轮以免重复呢?到目前为止，这是我所做的事情(将所有组合组合在一起):

 <?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;/* 输出:[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"] */ 

我的问题

有没有一种通用的方式将两对分配成几回合，而玩家却没有在同一回合中出现过一次以上?

示例

• 1 ^st 回合:12、34、56；
• 2 ^nd 回合:13、25、46 ...

解决方案

您可以使用此代码.它基于

玩家1永远不会移动，将位于第2位的玩家从数组中切出，并推入数组的末尾，这意味着它将到达第6位.

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...

解决方案

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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