如何实现100%符合规则的世界杯小组赛抽签算法？

算力阿峰

2026-8-13

实现100%符合规则的世界杯小组赛抽签算法

我花费大量时间尝试用JavaScript实现UEFA Champions League小组赛抽签功能，先后测试了5-7种算法，但均无法稳定成功（因随机打乱和选取导致成功率不稳定）。受挫放弃数月后，我尝试实现FIFA World Cup小组赛抽签，遇到了同样的问题，却发现原本用于世界杯的某一算法在欧冠场景下可成功运行。

我认为原因在于欧冠规则清晰固定：每组需包含各档球队，且同协会球队不能同组；而世界杯规则更为复杂，除每组包含各档球队、同足联球队不能同组外，还存在UEFA球队的动态规则——每组至少有1支、最多2支UEFA球队，其中5组有2支，3组有1支，现有算法无法处理这类动态规则。

我将算法逻辑举例说明：对每档球队打乱后，为每支球队筛选符合规则的可用分组，同时查看后续球队的可用分组，再统计拥有相同可用分组的球队数量。例如当前球队可用分组为[1,4]，另一球队可用分组仅为[4]，则分组4需预留，不能分配给当前球队；若有两支球队可用分组均为[1,3]，则分组1和3需预留。

可正常运行的欧冠抽签代码

Array.prototype.randomIndex = function () {
  return Math.floor(Math.random() * this.length);
};
Array.prototype.random = function () {
  return this[this.randomIndex()];
};
Array.prototype.shuffle = function () {
  return this.sort(() => Math.random() - .5);
};
const pots   = [[{"name":"Real Madrid","country":"Spain"},{"name":"Eintracht Frankfurt","country":"Germany"},{"name":"Manchester City","country":"England"},{"name":"AC Milan","country":"Italy"},{"name":"Bayern München","country":"Germany"},{"name":"Paris Saint-Germain","country":"France"},{"name":"FC Porto","country":"Portugal"},{"name":"Ajax","country":"Netherlands"}],[{"name":"Liverpool","country":"England"},{"name":"Chelsea","country":"England"},{"name":"FC Barcelona","country":"Spain"},{"name":"Juventus","country":"Italy"},{"name":"Atlético Madrid","country":"Spain"},{"name":"Sevilla","country":"Spain"},{"name":"RB Leipzig","country":"Germany"},{"name":"Tottenham Hotspur","country":"England"}],[{"name":"Borussia Dortmund","country":"Germany"},{"name":"FC Salzburg","country":"Austria"},{"name":"Shakhtar Donetsk","country":"Ukraine"},{"name":"Internazionale","country":"Italy"},{"name":"Napoli","country":"Italy"},{"name":"Benfica","country":"Portugal"},{"name":"Sporting CP Lisbon","country":"Portugal"},{"name":"Bayer Leverkusen","country":"Germany"}],[{"name":"Glasgow Rangers","country":"Scotland"},{"name":"Dinamo Zagreb","country":"Croatia"},{"name":"Olympique Marseille","country":"France"},{"name":"FC København","country":"Denmark"},{"name":"Club Brugge","country":"Belgium"},{"name":"Celtic","country":"Scotland"},{"name":"Viktoria Plzen","country":"Czechia"},{"name":"Maccabi Haifa","country":"Israel"}]];
const groups = new Array(8).fill().map(() => new Array(4));
function getAvailable(team, pot, execlude = null) {
  let availableGroups = groups.filter(g => g != execlude && g.every(t => !pot.includes(t)));
  availableGroups = availableGroups.filter(g => g.every(t => t.country != team.country));
  return availableGroups;
}
function getAvailableGroups(teams, pot) {
  let availableGroups = getAvailable(teams[0], pot);
  if (availableGroups.length == 1) return availableGroups;
  let available = [];
  checking: for (let group of availableGroups) {
    let leftNextAvailableGroups = teams.slice(1).map(t => getAvailable(t, pot, group));
    if (leftNextAvailableGroups.find(ag => !ag.length)) continue checking;
    let freeGroups = new Set;
    for (let nextTeamAvailableGroups of leftNextAvailableGroups) {
      if (nextTeamAvailableGroups.length == 1 && nextTeamAvailableGroups.includes(group)) continue checking;
      let samePossibilites = leftNextAvailableGroups.filter(ag => ag.length == nextTeamAvailableGroups.length && ag.every((g, i) => g == nextTeamAvailableGroups[i]));
      if (samePossibilites.length == nextTeamAvailableGroups.length && samePossibilites[0].includes(group)) continue checking;
      if (availableGroups.some(g => leftNextAvailableGroups.filter(ag => ag.length == 1).includes(g))) continue checking;
      if (samePossibilites.length > nextTeamAvailableGroups.length) continue checking;
      nextTeamAvailableGroups.forEach(g => freeGroups.add(g));
    }
    if (freeGroups.size != teams.length - 1) continue checking;
    available.push(group);
  }
  return available;
}
pots.forEach(pot => pot.shuffle());
let p = 0;
for (let pot of pots) {
  for (let i = 0; i < 8; i++) {
    if (!p) {
      groups[i][0] = pot[i];
      continue;
    }
    let group = getAvailableGroups(pot.slice(i), pot).random();
    group[p] = pot[i];
  }
  p++;
}