比赛问题

Question

我们有这个小任务来创建n支球队的比赛，每支球队必须在o球场上按照3条规则进行m场比赛：

1. 一个游戏不能玩超过一次
2. 一个团队不能与自己抗衡
3. 在比赛的任何给定时间，一支球队出战的时间差不能大于一个。

下面的代码解决了这个问题，但是显然很慢。我知道有一个解决方案快一百万倍（而且在C ++中也是如此，但我不相信这会产生超过一千倍的差异），但是不知道该代码。

有没有人建议更快地编写以下代码。进行回溯以寻找答案（允许比赛）是一种post悔。评估查看是否仍允许该锦标赛，如果锦标赛仍然有效，extend会（递归）从all_possible_games堆栈中添加游戏。 E指定一个空字段，仅在最后一轮才允许。对于2-30个不同领域的团队，该程序运行良好。但是在50个球场上有100个球队，每个球队10场比赛应该可以在0.001秒内解决。这个程序需要几个小时...

import math


def printtournament(tournament):
    for gameround in grouped(tournament, fields):
        for game in sorted(gameround, key=lambda x: x[0] if isinstance(x[0], int) else 0):
            if game[0] != 'E':
                print(game, end='')
        print()
    print()


def grouped(iterable, n):
    return zip(*[iter(iterable)]*n)


def allgames(teamcount):
    games = []
    for t in range(teamcount):
        for u in range(teamcount):
            if u is not t:
                game = (u, t)
                game = sorted(game, reverse=False)
                if game not in games:
                    games.append(game)
    return games


def evaluate(tournament, fieldcount, gamesperteam, teamcount):
    current_games_per_team = {}

    for i in range(teamcount):
        current_games_per_team[i] = 0
    current_games_per_team['E'] = 0
    gamehasbeenplayed = []
    current_games_per_team_round = {}
    for i in range(teamcount):
        current_games_per_team_round[i] = 0
    current_games_per_team_round['E'] = 0

    for gameround in grouped(tournament, fieldcount):
        teamhasplayed = []

        for game in (gameround):
            for t in game:
                if t in teamhasplayed and t is not 'E':
                    return False
                else:
                    teamhasplayed.append(t)
            if game in gamehasbeenplayed and game[0] is not 'E' and game[1] is not 'E':
                return False
            else:
                gamehasbeenplayed.append(game)

            current_games_per_team[int(game[0]) if isinstance(game[0], int) else 'E'] += 1
            current_games_per_team[int(game[1]) if isinstance(game[0], int) else 'E'] += 1
            current_games_per_team_round[int(game[0]) if isinstance(game[0], int) else 'E'] += 1
            current_games_per_team_round[int(game[1]) if isinstance(game[0], int) else 'E'] += 1

            for k, c in current_games_per_team.items():
                if c > gamesperteam and k is not 'E':
                    return False

        for k1, c in current_games_per_team_round.items():
            for k2, d in current_games_per_team_round.items():
                if abs(c - d) > 1 and k1 is not 'E' and k2 is not 'E':
                    return False
    return True

def extend(gamecount, games, teams, fields, gamesperteam):
    if gamecount < games:
        for game in all_possible_games:
            tournament[gamecount] = game
            for i in range(fieldrounds):
                if i > gamecount:
                    tournament[i] = ['E', 'E']
            if evaluate(tournament, fields, gamesperteam, teams):
                extend(gamecount+1, games, teams, fields, gamesperteam)
    else:
        printtournament(tournament)


teams = 30
fields = 4
gamesperteam = 2
games = int(teams/2*gamesperteam)
fieldrounds = int(math.ceil(games/fields)*fields)
all_possible_games = allgames(teams)
tournament = []
for i in range(fieldrounds):
    tournament.append(['E', 'E'])

if __name__ == '__main__':
    extend(0, games, teams, fields, gamesperteam)