比赛支架放置算法 [英] Tournament bracket placement algorithm

问题描述

由于对手的种子列表（例如种子1到16），我试图写一个算法，将导致头号种子打在这一轮的最低种子，第二种子打的第二个最低的种子等等。

Given a list of opponent seeds (for example seeds 1 to 16), I'm trying to write an algorithm that will result in the top seed playing the lowest seed in that round, the 2nd seed playing the 2nd-lowest seed, etc.

分组1和16，2和15等为匹配是相当容易的，但我还需要确保更高的种子将发挥下种子在随后的几轮。

Grouping 1 and 16, 2 and 15, etc. into "matches" is fairly easy, but I also need to make sure that the higher seed will play the lower seed in subsequent rounds.

与正确放置一个例子支架：

An example bracket with the correct placement:

1 vs 16
            1 vs 8
8 vs 9
                        1 vs 4
4 vs 13
            4 vs 5
5 vs 12
                                    1 vs 2
2 vs 15
            2 vs 7
7 vs 10
                        2 vs 3
3 vs 14
            3 vs 6
6 vs 11

正如你所看到的，种子1和2只满足在最后。

As you can see, seed 1 and 2 only meet up in the final.

推荐答案

我想出以下算法。它可能不是超高效的，但我不认为它真正需要的。它是用PHP编写的。

I've come up with the following algorithm. It may not be super-efficient, but I don't think that it really needs to be. It's written in PHP.

<?php
    $players = range(1, 32);
    $count = count($players);

    // Order players.
    for ($i = 0; $i < log($count / 2, 2); $i++) {
        $out = array();

        foreach ($players as $player) {
            $splice = pow(2, $i);

            $out = array_merge($out, array_splice($players, 0, $splice));

            $out = array_merge($out, array_splice($players, -$splice));
        }

        $players = $out;
    }

    // Print match list.
    for ($i = 0; $i < $count; $i++) {
        printf('%s vs %s<br />%s', $players[$i], $players[++$i], PHP_EOL);
    }
?>

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