数学之美番外篇:快排为什么那样快



数学之美番外篇:快排为什么那样快

1. 猜数字

我们先来玩一个猜数字游戏:我心里默念一个1~64之间的数,你来猜(你只能问答案是"是"或"否"的问题)。为了保证不论在什么情况下都能以尽量少的次数猜中,你应该采取什么策略呢?很显然,二分。先是猜是不是位于1~32之间,排除掉一半可能性,然后对区间继续二分。这种策略能够保证无论数字怎么跟你捉迷藏,都能在log_2{n}次以内猜中。用算法的术语来说就是它的下界是最好的。


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