Tanky Woo >> 随机化算法(1) -- 随机数



Tanky Woo » 随机化算法(1) — 随机数

接下来的几章(包括本章),我准备以连载的方式讲出来,主要用到的资料是上面推荐的那本书以及《算法导论》和网上的资源,内容是概率分析与随机算法。文章内大部分内容出自书中,我仅以汇总形式以及个人理解加以补充。如有纰漏,欢迎指出。

概率算法的一个基本特征是对所求解问题的同一实例用同一概率算法求解两次可能得到完全不同的效果。这两次求解问题所需的时间甚至所得到的结果可能会有相当大的差别。一般情况下,可将概率算法大致分为四类:数值概率算法,蒙特卡罗(Monte Carlo)算法,拉斯维加斯(Las Vegas)算法和舍伍德(Sherwood)算法。

随机数在概率算法设计中扮演着十分重要的角色。在现实计算机上无法产生真正的随机数,因此在概率算法中使用的随机数都是一定程度上随机的,即伪随机数

产生随机数最常用的方法是线性同余法。由线性同余法产生的随机序列a1,a2,…,an满足
1.a0=d
2.an=(b*an-1+c)mod m (n=1,2…….)
其中,b>0, c>=0, d>=m。d称为该随机序列的种子

一般情况下,取gcd(m, b)=1,因此可取b为一素数。


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