algorithm - 生成配对游戏的时间表

Question

我们有8名球员。

在一张桌子上玩 4 名玩家（两对）。

因此，每个玩家都需要与所有其他 7 名玩家配对，并让这些玩家作为对手的计数相同。

如果只是创建表并从列表中删除它，我们有：

Tour 1: (1,2) - (3,4) | (5,6) - (7,8)
Tour 2: (1,3) - (2,5) | (4,7) - (6,8)
.....................................
.....................................
Tour 7: (1,8) - (2,7) | (3,6) - (4,5)

但是一些付款人会比其他人经常遇到一些反对者。

我需要朝那个方向思考？

****更新**** 在 Jens Schauders 解决方案的情况下，我们将进行 7 轮。如果玩家 2 与对手对弈，我们将有 3 次对手 4 和 1 次对手 7。

如果在此模式中拆分对

       TABLE 1 |  TABLE 2

Pair1: 1    2  |  3    4
      ------------------
Pair2: 5    6  |  7    8

错在哪里？

Answer 1

我认为您正在寻找的算法有一个简单的可视化：

想象一张长桌，对手坐在对面：

1    2    3    4
----------------
5    6    7    8

现在，对于每一轮新的回合，每个人都移动到他左边的位置。可能在桌子的另一边，除了一个例外：玩家一号保持她的座位。所以下一轮看起来像这样

1    5    2    3    
----------------
6    7    8    4

如果您现在将长桌分成两部分，您将获得适合您的小桌的配对。

关于更新的问题

为了使对手分布更均匀，可以尝试以不同的方式拆分大表，例如从第一列和第四列构建一个小表，从第 2+3 列构建第二个小表

Answer 2

您可以在 4 支球队之间进行 6 场独特的比赛。有 7 种可能的配对，因此有 42 种独特的游戏。

每个玩家只与其他玩家配对一次，并且与他们中的每个人精确对战 6 次。

列表：

Pairs 01: (1,2),(3,4),(5,6),(7,8)
PairRound 1:
GameRound 01: (1,2) - (3,4) | (5,6) - (7,8)
GameRound 02: (1,2) - (7,8) | (3,4) - (5,6)
GameRound 03: (1,2) - (5,6) | (3,4) - (7,8)

Pairs 02: (1,3),(2,4),(5,7),(6,8)
PairRound 2:
GameRound 04: (1,3) - (2,4) | (5,7) - (6,8)
GameRound 05: (1,3) - (6,8) | (2,4) - (5,7)
GameRound 06: (1,3) - (5,7) | (2,4) - (6,8)

Pairs 03: (1,4),(2,3),(5,8),(6,7)
PairRound 3:
GameRound 07: (1,4) - (2,3) | (6,7) - (5,8)
GameRound 08: (1,4) - (5,8) | (2,3) - (6,7)
GameRound 09: (1,4) - (6,7) | (2,3) - (5,8)

Pairs 04: (1,5),(2,6),(3,7),(4,8)
PairRound 4:
GameRound 10: (1,5) - (2,6) | (3,7) - (4,8)
GameRound 11: (1,5) - (4,8) | (2,6) - (3,7)
GameRound 12: (1,5) - (3,7) | (2,6) - (4,8)

Pairs 05: (1,6),(2,5),(3,8),(4,7)
PairRound 5:
GameRound 13: (1,6) - (2,5) | (3,8) - (4,7)
GameRound 14: (1,6) - (4,7) | (2,5) - (3,8)
GameRound 15: (1,6) - (3,8) | (2,5) - (4,7)

Pairs 06: (1,7),(2,8),(3,5),(4,6)
PairRound 6:
GameRound 16: (1,7) - (2,8) | (3,5) - (4,6)
GameRound 17: (1,7) - (4,6) | (2,8) - (3,5)
GameRound 18: (1,7) - (3,5) | (2,8) - (4,6)

Pairs 07: (1,8),(2,7),(3,6),(4,5)
PairRound 8:
GameRound 19: (1,8) - (2,7) | (3,6) - (4,5)
GameRound 20: (1,8) - (4,5) | (2,7) - (3,6)
GameRound 21: (1,8) - (3,6) | (2,7) - (4,5)

Answer 3

下面是两个时间表。第一个时间表是 2 轮循环固定合作伙伴时间表。这是一个平衡的 2 轮循环“对”赛程。或者，另一种说法是我们正在安排“对”中的“对”。我想这就是你要找的吗？

第二个赛程是一个“平衡的”2 轮循环赛“单打”赛程，有 8 名球员（每个球员都是一个团队）。

注意：在这两个时间表上，所有球员/球队都轮流通过所有表。没有球员/球队固定在一个固定的位置，这对大多数联赛来说都是不受欢迎的，因为它会造成不平衡的时隙分布。该线程上发布的其他两个答案将单个团队锁定在单个时间段中，然后将其他 7 个团队轮换通过该时间段。

下面的 PAIRS-4 时间表是固定的合作伙伴时间表。我们还有一个 8 人轮换合作伙伴的时间表。在每轮循环赛中，所有球员都与其他 7 名球员中的每一个搭档一次，并且与所有其他球员正好交手两次。

PAIRS-4 SCHEDULE                     Date 8/4/14            
-    
DATE   DAY  TIME   LOCATION     GM#   HOME  v  AWAY
Week 1         
AUG  4 MON  6:00pm Table-1       1  #1 & #2 v #7 & #8
AUG  4 MON  6:00pm Table-2       1  #3 & #4 v #5 & #6
Week 2
AUG 11 MON  6:00pm Table-1       2  #7 & #8 v #3 & #4
AUG 11 MON  6:00pm Table-2       2  #5 & #6 v #1 & #2
Week 3    
AUG 18 MON  6:00pm Table-1       3  #1 & #2 v #3 & #4
AUG 18 MON  6:00pm Table-2       3  #5 & #6 v #7 & #8
Week 4
AUG 25 MON  6:00pm Table-1       4  #5 & #6 v #3 & #4
AUG 25 MON  6:00pm Table-2       4  #7 & #8 v #1 & #2
Week 5        
SEP  1 MON  6:00pm Table-1       5  #1 & #2 v #5 & #6
SEP  1 MON  6:00pm Table-2       5  #3 & #4 v #7 & #8
Week 6    
SEP  8 MON  6:00pm Table-1       6  #7 & #8 v #5 & #6
SEP  8 MON  6:00pm Table-2       6  #3 & #4 v #1 & #2
-    
========================================================
-
SINGLES-8 SCHEDULE               Date 8/5/14 
-
DATE   DAY  TIME    LOCATION   GM#  HOME v AWAY
Week 1
AUG  5 TUE  6:00pm  Table-1     1   #1 v #8
AUG  5 TUE  6:00pm  Table-2     1   #2 v #7
AUG  5 TUE  6:00pm  Table-3     1   #3 v #6
AUG  5 TUE  6:00pm  Table-4     1   #4 v #5
Week 2    
AUG 12 TUE  6:00pm  Table-1     2   #5 v #2
AUG 12 TUE  6:00pm  Table-2     2   #8 v #6
AUG 12 TUE  6:00pm  Table-3     2   #7 v #1
AUG 12 TUE  6:00pm  Table-4     2   #3 v #4
Week 3
AUG 19 TUE  6:00pm  Table-1     3   #2 v #3
AUG 19 TUE  6:00pm  Table-2     3   #5 v #7
AUG 19 TUE  6:00pm  Table-3     3   #4 v #8
AUG 19 TUE  6:00pm  Table-4     3   #6 v #1
Week 4
AUG 26 TUE  6:00pm  Table-1     4   #6 v #4
AUG 26 TUE  6:00pm  Table-2     4   #1 v #5
AUG 26 TUE  6:00pm  Table-3     4   #7 v #3
AUG 26 TUE  6:00pm  Table-4     4   #8 v #2
Week 5
SEP  2 TUE  6:00pm  Table-1     5   #3 v #5
SEP  2 TUE  6:00pm  Table-2     5   #4 v #1
SEP  2 TUE  6:00pm  Table-3     5   #2 v #6
SEP  2 TUE  6:00pm  Table-4     5   #7 v #8
Week 6
SEP  9 TUE  6:00pm  Table-1     6   #6 v #7
SEP  9 TUE  6:00pm  Table-2     6   #4 v #2
SEP  9 TUE  6:00pm  Table-3     6   #5 v #8
SEP  9 TUE  6:00pm  Table-4     6   #1 v #3
Week 7
SEP 16 TUE  6:00pm  Table-1     7   #7 v #4
SEP 16 TUE  6:00pm  Table-2     7   #8 v #3
SEP 16 TUE  6:00pm  Table-3     7   #2 v #1
SEP 16 TUE  6:00pm  Table-4     7   #5 v #6
Week 8
SEP 23 TUE  6:00pm  Table-1     8   #7 v #2
SEP 23 TUE  6:00pm  Table-2     8   #6 v #3
SEP 23 TUE  6:00pm  Table-3     8   #5 v #4
SEP 23 TUE  6:00pm  Table-4     8   #8 v #1
Week 9
SEP 30 TUE  6:00pm  Table-1     9   #6 v #8
SEP 30 TUE  6:00pm  Table-2     9   #1 v #7
SEP 30 TUE  6:00pm  Table-3     9   #4 v #3
SEP 30 TUE  6:00pm  Table-4     9   #2 v #5
Week 10
OCT  7 TUE  6:00pm  Table-1    10   #7 v #5
OCT  7 TUE  6:00pm  Table-2    10   #8 v #4
OCT  7 TUE  6:00pm  Table-3    10   #1 v #6
OCT  7 TUE  6:00pm  Table-4    10   #3 v #2
Week 11
OCT 14 TUE  6:00pm  Table-1    11   #5 v #1
OCT 14 TUE  6:00pm  Table-2    11   #3 v #7
OCT 14 TUE  6:00pm  Table-3    11   #2 v #8
OCT 14 TUE  6:00pm  Table-4    11   #4 v #6
Week 12
OCT 21 TUE  6:00pm  Table-1    12   #1 v #4
OCT 21 TUE  6:00pm  Table-2    12   #6 v #2
OCT 21 TUE  6:00pm  Table-3    12   #8 v #7
OCT 21 TUE  6:00pm  Table-4    12   #5 v #3
Week 13
OCT 28 TUE  6:00pm  Table-1    13   #2 v #4
OCT 28 TUE  6:00pm  Table-2    13   #8 v #5
OCT 28 TUE  6:00pm  Table-3    13   #3 v #1
OCT 28 TUE  6:00pm  Table-4    13   #7 v #6
Week 14
NOV  4 TUE  6:00pm  Table-1    14   #3 v #8
NOV  4 TUE  6:00pm  Table-2    14   #1 v #2
NOV  4 TUE  6:00pm  Table-3    14   #6 v #5
NOV  4 TUE  6:00pm  Table-4    14   #4 v #7
-               
-                 # # # # #    
-

您可以将上面的时间表复制并粘贴到您的文字处理器中，然后使用“搜索和替换”将球员号码替换为真实姓名。您还可以编辑时间表，即更改日期和时间、添加注释、图形、每个玩家的联系信息等。