Friday, November 27, 2015

Horse Race - 赛马问题



http://lixinzhang.github.io/jiu-zhang-suan-fa-mian-shi-ti-zong-jie.html
有25匹马,有一个5个赛道的马场,每场比赛可以决出5匹马的排名,假设每匹马发挥稳定,且不会出现名次相同的情况。问,如果要知道25匹马中跑得最快的马,需要几场比赛?如果需要知道跑得第二快的马,需要几场比赛?第三快的呢?

分析

  1. 最快的,需要6次。
    • 每五匹赛一次(5次),每次的第一名,再一起赛一次(1次)
  2. 第二快的,需要7次。
    • 每五匹赛一次(5次),每次的第一名,再一起赛一次(1次)
    • 最快的那组的第二名,与上次的第二名,跑一次。(1次)
  3. 第三快的,需要7次。
    • 每五匹赛一次(5次),每次的第一名,再一起赛一次(1次)
    • 最快的那组的第二、三名,与上次的第二名那组里的第二名,与上次的第二、第三名一起跑一次。

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