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N players with 2 fields
送交者: 零加一中 2009年06月30日04:54:07 于 [灵机一动] 发送悄悄话
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? --------------------------------------------------------------------- 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. ---------------------------------------------------------------------- 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. -------------------------------------------------------------------------- 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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