ALgorithm - Random


https://zhengyang2015.gitbooks.io/lintcode/random_generator.html
给一个1到3的random generator,构造一个1到n的random generator。


用3进制数来求解。首先求出n至少需要几位3进制数来表示,假设需要x位。然后利用1到3的random generator来产生依次产生每一位上的随机数(因为3进制每一位上是0到2,所以要将得到的随机数-1)。再将得到的随机数转化为十进制整数。因为x位3进制的数能表示的十进制的数的范围是0~3^x - 1,因此得到的随机数可能比n大。如果得到的结果大于n,则重新产生随机数。

如果调用这个n random generator很多次,很可能产生很多次重复的随机数。因此,可以将得到的合法3进制的数及其对应的十进制的数保存在一个table里来优化时间。每次产生一个随机数,就和n比较,如果大于n,则重新产生,否则去table寻找其对应的十进制数。如果没有找到,则说明该随机数第一次产生,将该随机数的3进制及其十进制形式保存在table里。

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