java蒙特卡洛演算法求PI值（視覺化）及三門問題
阿新 • • 發佈：2018-12-25
蒙特卡洛演算法求PI值
工具類
package com.egeo.jframetext;
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.FontMetrics;
import java.awt.Graphics2D;
import java.awt.Image;
import java.awt.geom.Ellipse2D;
import java.awt.geom.Rectangle2D;
import javax.swing.ImageIcon;
public class AlgoVisHelper 檢視層
package com.egeo.jframetext;
import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.RenderingHints;
import javax.swing.JFrame;
import javax.swing.JPanel;
public class AlgoFrame extends JFrame{
private int canvasWidth;
private int canvasHeight;
public AlgoFrame(String title, int canvasWidth, int canvasHeight){
super(title);
this.canvasWidth = canvasWidth;
this.canvasHeight = canvasHeight;
AlgoCanvas canvas = new AlgoCanvas();
setContentPane(canvas);
pack();
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
setResizable(false);
setVisible(true);
}
public AlgoFrame(String title){
this(title, 1024, 768);
}
public int getCanvasWidth(){return canvasWidth;}
public int getCanvasHeight(){return canvasHeight;}
// data
private MonteCarloPiData data;
public void render(MonteCarloPiData data){
this.data = data;
repaint();
}
private class AlgoCanvas extends JPanel{
public AlgoCanvas(){
// 雙快取
super(true);
}
@Override
public void paintComponent(Graphics g) {
super.paintComponent(g);
Graphics2D g2d = (Graphics2D)g;
// 抗鋸齒
RenderingHints hints = new RenderingHints(
RenderingHints.KEY_ANTIALIASING,
RenderingHints.VALUE_ANTIALIAS_ON);
hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
g2d.addRenderingHints(hints);
// 具體繪製
AlgoVisHelper.setStrokeWidth(g2d, 3);
AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
Circle circle = data.getCircle();
AlgoVisHelper.strokeCircle(g2d, circle.getX(), circle.getY(), circle.getR());
for(int i = 0 ; i < data.getPointsNumber() ; i ++){
Point p = data.getPoint(i);
//判斷點是否在圓裡
if(circle.contain(p))
AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
else
AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
AlgoVisHelper.fillCircle(g2d, p.x, p.y, 3);
}
}
@Override
public Dimension getPreferredSize(){
return new Dimension(canvasWidth, canvasHeight);
}
}
}
實體類
package com.egeo.jframetext;
import java.awt.Point;
public class Circle {
private int x, y, r;
public Circle(int x, int y, int r){
this.x = x;
this.y = y;
this.r = r;
}
public int getX(){ return x; }
public int getY(){ return y; }
public int getR(){ return r; }
public boolean contain(Point p){
return Math.pow(p.x - x, 2) + Math.pow(p.y - y, 2) <= r*r;
}
}
控制層
package com.egeo.jframetext;
import java.awt.EventQueue;
import java.awt.Point;
public class AlgoVisualizer {
private static int DELAY = 40;
private MonteCarloPiData data;
private AlgoFrame frame;
private int N;
public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
//判斷高度寬度是否相等（是否為正方形）
if(sceneWidth != sceneHeight)
throw new IllegalArgumentException("This demo must be run in a square window!");
this.N = N;
//在正方形內畫圓
Circle circle = new Circle(sceneWidth/2, sceneHeight/2, sceneWidth/2);
data = new MonteCarloPiData(circle);
// 初始化檢視
EventQueue.invokeLater(() -> {
frame = new AlgoFrame("Monte Carlo", sceneWidth, sceneHeight);
new Thread(() -> {
run();
}).start();
});
}
public void run(){
for(int i = 0 ; i < N ; i ++){
//每100次進行一次繪製
if( i % 100 == 0) {
frame.render(data);
//等待時間
AlgoVisHelper.pause(DELAY);
//控制檯列印PI值
System.out.println(data.estimatePi());
}
int x = (int)(Math.random() * frame.getCanvasWidth());
int y = (int)(Math.random() * frame.getCanvasHeight());
data.addPoint(new Point(x, y));
}
}
public static void main(String[] args) {
int sceneWidth = 800;
int sceneHeight = 800;
int N = 20000;
AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N);
}
}
邏輯處理類
package com.egeo.jframetext;
import java.awt.Point;
import java.util.LinkedList;
public class MonteCarloPiData {
private Circle circle;
private LinkedList<Point> points;
private int insideCircle = 0;
public MonteCarloPiData(Circle circle){
this.circle = circle;
points = new LinkedList<Point>();
}
public Circle getCircle(){
return circle;
}
public int getPointsNumber(){
return points.size();
}
public Point getPoint(int i){
if(i < 0 || i >= points.size())
throw new IllegalArgumentException("out of bound in getPoint!");
return points.get(i);
}
public void addPoint(Point p){
points.add(p);
//是否在圓內
if(circle.contain(p))
insideCircle ++;
}
public double estimatePi(){
if(points.size() == 0)
return 0.0;
int circleArea = insideCircle;
int squareArea = points.size();
return (double)circleArea * 4 / squareArea;
}
}
程式執行效果
蒙特卡洛演算法求解三門問題
package com.egeo.jframetext;
public class ThreeGatesExperiment {
//模擬次數
private int N;
public ThreeGatesExperiment(int N){
if(N <= 0)
throw new IllegalArgumentException("N must be larger than 0!");
this.N = N;
}
public void run(boolean changeDoor){
int wins = 0;
for(int i = 0 ; i < N ; i ++)
if(play(changeDoor))
wins ++;
System.out.println(changeDoor ? "Change" : "Not Change");
System.out.println("winning rate: " + (double)wins/N);
}
private boolean play(boolean changeDoor){
// Door 0, 1, 2
//隨機中獎的門
int prizeDoor = (int)(Math.random() * 3);
//觀眾選中的門
int playerChoice = (int)(Math.random() * 3);
//是否換門
if( playerChoice == prizeDoor)
return changeDoor ? false : true;
else
return changeDoor ? true : false;
}
public static void main(String[] args) {
int N = 10000000;
ThreeGatesExperiment exp = new ThreeGatesExperiment(N);
exp.run(true);
System.out.println();
exp.run(false);
}
}
