蒙特卡罗方法计算圆周率

前几天读到了一篇网志：蒙特卡罗方法入门，http://www.ruanyifeng.com/blog/2015/07/monte-carlo-method.html

其中介绍了用概率计算圆周率的方法，所以就用程序做了以下尝试。

作为常量的PI值的近似在Math.PI中为3.141592653589793。

Ⅰ.方形中的所有像素计算

package yumu.probability.montecarlo;public class CalculatePI {  private static final int RADIUS = 10000;      public static void main(String[] args) {        int circle = 0;    for(int i = 0; i < RADIUS; ++i){      for(int j = 0; j < RADIUS; ++j){        if(i*i + j*j < RADIUS*RADIUS){          ++circle;        }      }    }        double quarterPI = (double)circle / (RADIUS * RADIUS);    System.out.println(quarterPI * 4);  }  }

运行结果如下：

3.14199016

Ⅱ.方形中的随机像素计算

package yumu.probability.montecarlo;public class RandomPI {  private static final int QUANTITY = 10000000;      public static void main(String[] args) {        double x, y;        int circle = 0;    for(long i = 0; i < QUANTITY; ++i){      x = Math.random();      y = Math.random();      if(x*x + y*y < 1){        ++circle;      }    }        double quarterPI = (double)circle / QUANTITY;    System.out.println(quarterPI * 4);  }  }

多次运行结果如下：

3.14113443.1422143.1410763.1407648

Ⅲ.方形中的随机像素求平均值

package yumu.probability.montecarlo;public class RandomTwicePI {  private static final int COUNT = 100;  private static final int QUANTITY = 1000000;    public static void main(String[] args) {        double sum = 0;    for(int i = 0; i < COUNT; ++ i){      sum += randomPI();    }        double pi = sum / COUNT;    System.out.println(pi);  }      private static double randomPI(){    double x, y;        int circle = 0;    for(long i = 0; i < QUANTITY; ++i){      x = Math.random();      y = Math.random();      if(x*x + y*y < 1){        ++circle;      }    }        double quarterPI = (double)circle / QUANTITY;    return quarterPI*4;  }  }

多次运行结果如下：

3.14175815999999933.1414950800000013.1415940399999998

Ⅳ.方体中的所有小方体计算

package yumu.probability.montecarlo;public class CalculateCubePI {  private static final int RADIUS = 1000;      public static void main(String[] args) {        int sphere = 0;    for(int i = 0; i < RADIUS; ++i){      for(int j = 0; j < RADIUS; ++j){        for(int k = 0; k < RADIUS; ++k){          if(i*i + j*j + k*k < RADIUS*RADIUS){            ++sphere;          }        }      }    }        double oneInSixOfPI = (double)sphere / (RADIUS * RADIUS * RADIUS);    System.out.println(oneInSixOfPI * 6);  }}

运行结果如下：

3.148658436

Ⅴ.莱布尼茨公式计算

参考这个级数：Leibniz formula for π, https://en.wikipedia.org/wiki/Leibniz_formula_for_%CF%80

package yumu.probability.montecarlo;public class LeibnizSeriesPI {  private static final int COUNT = 100000000;    public static void main(String[] args) {        double quarterPI = 1;    for(int i = 1; i < COUNT; ++i){      double temp = i%2==0 ? 1 : -1;      temp /= i*2 + 1;      quarterPI += temp;    }        System.out.println(quarterPI * 4);  }}

运行结果如下：