麻雀大会でどのように席を入れ替えれば毎回別の人と対戦できるか？

PLAYERS = 16
TABLES = PLAYERS // 4

# matched[i] は i 番目の人が対戦済みの人のセット
matched = [set() for _ in range(PLAYERS)]

# seats[i] は i 番目の卓に座っている人のリスト
seats = [[] for _ in range(TABLES)]

# player が table に座れるか？
def can_seat(player, table):
    # 満席か？
    if len(seats[table]) == 4: return False
    # 対戦済みの人がいるか？
    return not(matched[player] & set(seats[table]))

# 1つ前の卓が空いているのに、次の卓に座ろうとしたら終わり
#（残りは卓の入れ替えでしかないので）
def no_more():
    prev_not_seated = False
    for i in range(TABLES):
        seated = len(seats[i]) > 0
        if seated and prev_not_seated:
            return True
        prev_not_seated = not(seated)
    return False

# 確定した席で対戦済み表を更新
def update_matched():
    for s in seats:
        for p in s:
            matched[p] |= set(s)

# 座席表を出力
def print_seats(game):
    print("{}ゲーム目".format(game))
    game += 1
    for i in range(TABLES):
        s = ', '.join(map(lambda p: "{:2}".format(p+1), seats[i]))
        print('  {}番卓: {}'.format(i + 1, s))
    print()

# player が座れる卓に座る
def take_seat(player, game):
    if no_more():
        return False

    # 全員座ったら出力して終了
    if player == PLAYERS:
        print_seats(game)
        update_matched()
        return True

    # 入れる卓に入る
    for t in range(TABLES):
        if can_seat(player, t):
            # 次のプレイヤーへ
            seats[t].append(player)
            complete = take_seat(player + 1, game)
            seats[t].remove(player)
            if complete: return True

if __name__ == '__main__':
    game = 1
    while take_seat(0, game):
        game += 1