N 个羽毛球运动员,编号1,2,3,..., N, 打循环赛。有两个场地可以应用。
假定,每场比赛的时间是相等的。怎样分配场地使得最短时间内完成所有
比赛?
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First N-2 matches in field 1:
1-3, 1-4, ..., 1-N
First N-2 matches in field 2:
2-4, 2-5, ..., 2-N, 2-3
At this time, players 1 and 2 finished all matches except 1-2.
Next N-4 matches in field 1:
3-5, 3-6, ..., 3-N
Next N-4 matches in field 2:
4-6, 4-7, ..., 4-N, 4-5
At this time, players 3 and 4 also finished all matches except 3-4.
Continue doing this, end situation depends on N odd or even.
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For odd N (=2K+1).
K-1 pairs need match between each two:
1-2, 3-4, ..., (2K-3)-(2K-2).
Three players need matches among them: 2K-1, 2K, 2K+1. It is straightforward to finish.
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For even (=K).
K-1 pairs need match between each two:
1-2, 3-4, ..., (2K-3)-(2K-2).
Two players need matches between them: 2K-1, 2K. It is straightforward to finish.
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