巴丰投针算法的模拟

女爷i 2022-06-17 04:58 113阅读 0赞

To run the Buffon needle experiment, we have to work a little harder. When you throw a die, it has to come up with one of six faces. When throwing a needle, however, there are many possible outcomes. You must generate two random numbers: one to describe the starting position and one to describe the angle of the needle with the x - axis.

Then you need to test whether the needle touches a grid line. Stop after 10,000 tries.

Let us agree to generate the lower point of the needle. Its x - coordinate is irrelevant, and you may assume its y - coordinate ylow to be any random number between 0 and 2. However, because it can be a random floating - point number, we use the nextDouble method of the Random class. It returns a random floating - point number between 0 and 1. Multiply by 2 to get a random number between 0 and 2.

The angle α between the needle and the x - axis can be any value between 0 degrees and 180 degrees. The upper end of the needle has y – coordinate

yhigh=ylog+sin(a);

The needle is a hit if yhigh is at least 2. See Figur below:

![0_1322489597Fv84.gif][]

实现原码如下:

import java.util.Random;
    
    
    public class NeedleTest {
    
    	public static void main(String[] args) {
    		Needle n=new Needle();
    		final int COUNT1=1000;
    		final int COUNT2=10000000;
    		
    		for(int i=1;i<=COUNT1;i++){
    			n.drop();
    		}
    		System.out.printf("尝试:%d,命中的次数比率为:%8.5f",COUNT1,(double)n.getTries()/n.getHits());
    		
    		for(int i=COUNT1+1;i<=COUNT2;i++){
    			n.drop();
    		}
    		System.out.printf("尝试:%d,命中的次数比率为:%8.5f",COUNT2,(double)n.getTries()/n.getHits());
    	}
    }
    
    
    class Needle{
    	private Random random;    //随机数生成器
    	private int hits;         //击中次数
    	private int tries;        // 尝试次数
    	
    	public Needle(){
    		this.hits=0;
    		this.tries=0;
    		random=new Random();
    	}
    	
    	/**
    	 * 获取针压线的次数
    	 */
    	public int getHits(){
    		return hits;
    	}
    	/**
    	 * 获取投什总次数
    	 */
    	public int getTries(){
    		return tries;
    	}
    	/**
    	 * 往等距线上投针，并记录下针是否压线
    	 * 业务实现: 1. 随机生成针的 最下端底坐标y值
    	 *           2. 随机生成针的角度
    	 *           3. 计算针的上端的位置
    	 */
    	public void drop(){
    		double ylow=2*random.nextDouble();
    		double angle=180*random.nextDouble();
    		//计算针的上端y位置
    		//Math.toRadians(angle): Converts an angle measured in degrees to an approximately equivalent angle measured in radians
    		double yhigh=ylow+Math.sin(Math.toRadians(angle));
    		if(yhigh>=2){
    			hits++;
    		}
    		tries++;
    	}
    }

[0_1322489597Fv84.gif]: /images/20220617/ebd7dbdafe814db7a0444af7e91ee4d4.png