这个程序有错误吗？计算 PI 模拟投掷飞镖 JAVA

Question

我应该编写一个程序，通过模拟在正方形的内切圆上投掷飞镖来计算 PI。它将为 x 和 y 值（坐标点）生成随机数，如果 x^2+y^ 小于或等于 1，则飞镖确实击中了圆圈，否则没有（未命中）。 然后它使用以下公式计算 pi：pi = 4 *（命中/总投掷）。 这类似于布冯的针头实验。 正如您在下面看到的，我已经编写了代码，但是当我编译它时，pi 的值甚至没有接近 3.14 :(

 /**
 * This program is intended to calculate the value of pi by simulating throwing darts at a dart                  *board.
 * 
 * @author Nataly Carbonell
 * @version 12/13/2014
 */
import java.util.Scanner;
import java.util.Random;
public class Darts
{
public static double[] calcPi(int d, int t)
{


     int hit = 0;
     int miss = 0;
     double [] posX = new double[d];
     double [] posY = new double[d];
     double[] pi = new double[t];
    for(int i = 0; i < t; i++)
    {
        for(int index = 0; index < d; index++)
        {   
            posX[index] = 2 * Math.random() + - 1;
            posY[index] = 2 * Math.random() + - 1;





            if((Math.pow(posX[index], 2) + Math.pow(posY[index], 2)) <= 1)
            {
                hit++;
            }

            else if ((Math.pow(posX[index], 2) + Math.pow(posY[index], 2))> 1)
            {
                miss++;
            }

    }

    pi[i] = (4 * (hit / d));
    }
   return pi;
}

  public static double calcPiAverage(double[] p, double t)
   {
    double average = 0;
    double sum = 0;
    for(int i = 0; i < t; i++)
    {
      sum += p[i];
    }
    average = sum / t;
    return average;
    }

    public static void printOutput(double [] p, double ave, int t)
    {
    for(int i = 0; i < t; i++)
    {
        System.out.print("Trial [" + i + "]: pi = ");
        System.out.printf("%5.5f%n", p[i]);


    }
    System.out.printf("Estimate of pi = %5.5f", ave);
   }

   public static void main(String[] args)
  {
   Scanner in = new Scanner(System.in);

   System.out.println("How many darts per trial? ");
   int darts = in.nextInt();
   System.out.println("How many trials? ");
   int trials = in.nextInt();

   double [] pi = new double[trials];
   pi = calcPi(darts, trials);

   double piAverage = calcPiAverage(pi, trials);

   printOutput(pi, piAverage, trials);



    }
 }

Answer 1

主要问题可能是您的整数除法：将您的hit 和/或d 转换为double，然后在这里取比率：(4 * (hit / d))。如果我正确理解您的代码，您可能还想在index 循环之外但在i 循环内重置hit。

再想一想：这种估计 pi ​​的蒙特卡洛方法收敛极其缓慢，因此您可以采取任何措施来加快速度。由于您可以根据hit 和d 的值计算miss，因此您不需要else if 子句。而且由于您根本不使用miss，因此您甚至不需要计算它。 （你也可以通过只在正 xy 象限中投掷飞镖来做得更好，但我在下面的代码中没有这样做）。

这是我编辑的代码：

 /**
 * This program is intended to calculate the value of pi by simulating throwing darts at a dart                  *board.
 * 
 * @author Nataly Carbonell
 * @version 12/13/2014
 */
import java.util.Scanner;
import java.util.Random;
public class Darts
{
public static double[] calcPi(int d, int t)
{


     int hit = 0;
     int miss = 0;
     double [] posX = new double[d];
     double [] posY = new double[d];
     double[] pi = new double[t];
    for(int i = 0; i < t; i++)
    {
        hit = 0;
        for(int index = 0; index < d; index++)
        {   
            posX[index] = 2 * Math.random() + - 1;
            posY[index] = 2 * Math.random() + - 1;

            if((Math.pow(posX[index], 2) + Math.pow(posY[index], 2)) <= 1)
            {
                hit++;
            }

    }

    pi[i] = (4 * ((double)hit / d));
    }
   return pi;
}

  public static double calcPiAverage(double[] p, double t)
   {
    double average = 0;
    double sum = 0;
    for(int i = 0; i < t; i++)
    {
      sum += p[i];
    }
    average = sum / t;
    return average;
    }

    public static void printOutput(double [] p, double ave, int t)
    {
    for(int i = 0; i < t; i++)
    {
        System.out.print("Trial [" + i + "]: pi = ");
        System.out.printf("%5.5f%n", p[i]);


    }
    System.out.printf("Estimate of pi = %5.5f", ave);
   }

   public static void main(String[] args)
  {
   Scanner in = new Scanner(System.in);

   System.out.println("How many darts per trial? ");
   int darts = in.nextInt();
   System.out.println("How many trials? ");
   int trials = in.nextInt();

   double [] pi = new double[trials];
   pi = calcPi(darts, trials);

   double piAverage = calcPiAverage(pi, trials);

   printOutput(pi, piAverage, trials);



    }
 }