用概率算法求pi值

基本思想：以坐标原点为圆心作一个半径为1的单位圆，再作一个正方形与此圆相切（其实是否相切不重要，此处只是为了计算方便）。在这个正方形内任取n个点，并比较判断是否落在圆内，将落在圆内的点计作k，那么n与k的比值就可以看成正方形和圆的面积之比。即圆周率PI=4*k/n。
 源码如下：

 

 

#include "stdafx.h"

#include "stdio.h"

#include "time.h"

 

const unsigned long maxshort = 65536L;

const unsigned long multiplier = 1194211693L;

const unsigned long adder = 12345L;

 

class RandomNumber

{

private:

       unsigned long randSeed;

public:

       RandomNumber(unsigned long s = 0);

       unsigned short Random(unsigned long n);

       double fRandom(void);

};

 

RandomNumber::RandomNumber(unsigned long s)

{

       if(s == 0)

              randSeed = time(0);

       else

              randSeed = s;

}

 

unsigned short RandomNumber::Random(unsigned long n)

{

       randSeed = multiplier * randSeed + adder;

       return(unsigned short)((randSeed >> 16) % n);

}

 

double RandomNumber::fRandom(void)

{

       return Random(maxshort)/double(maxshort);

}

 

double Darts(long n)

{

       static RandomNumber dart;

       int k=0;

       for(int i = 1; i <= n; i++)

       {

              double x = dart.fRandom();

              double y = dart.fRandom();

              if(x*x + y*y <= 1) k++;

       }

       return 4*(k/double(n));

}

 

int main(int argc, char* argv[])

{

       long n = 10000000;       //1000万

//     long n = 100000000; //1亿

//     long n = 1000000000; //10亿

       double pi = Darts(n);

       printf("%.10f/n",pi);

}