蒙特卡洛演算法求PI
利用蒙特卡洛法隨機生成任意點，求出PI
原始碼：
import java.awt.*;
import java.util.LinkedList;
import javax.swing.*;
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);
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);
}
}
}
import javax.swing.*;
import java.awt.*;
import java.awt.geom.Ellipse2D;
import java.awt.geom.GeneralPath;
import java.awt.geom.Line2D;
import java.awt.geom.Rectangle2D;
import java.lang.InterruptedException;
public class AlgoVisHelper {
private AlgoVisHelper(){}
public static final Color Red = new Color(0xF44336);
public static final Color Pink = new Color(0xE91E63);
public static final Color Purple = new Color(0x9C27B0);
public static final Color DeepPurple = new Color(0x673AB7);
public static final Color Indigo = new Color(0x3F51B5);
public static final Color Blue = new Color(0x2196F3);
public static final Color LightBlue = new Color(0x03A9F4);
public static final Color Cyan = new Color(0x00BCD4);
public static final Color Teal = new Color(0x009688);
public static final Color Green = new Color(0x4CAF50);
public static final Color LightGreen = new Color(0x8BC34A);
public static final Color Lime = new Color(0xCDDC39);
public static final Color Yellow = new Color(0xFFEB3B);
public static final Color Amber = new Color(0xFFC107);
public static final Color Orange = new Color(0xFF9800);
public static final Color DeepOrange = new Color(0xFF5722);
public static final Color Brown = new Color(0x795548);
public static final Color Grey = new Color(0x9E9E9E);
public static final Color BlueGrey = new Color(0x607D8B);
public static final Color Black = new Color(0x000000);
public static final Color White = new Color(0xFFFFFF);
public static void strokeCircle(Graphics2D g, int x, int y, int r){
Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
g.draw(circle);
}
public static void fillCircle(Graphics2D g, int x, int y, int r){
Ellipse2D circle = new Ellipse2D.Double(x-r, y-r, 2*r, 2*r);
g.fill(circle);
}
public static void strokeRectangle(Graphics2D g, int x, int y, int w, int h){
Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
g.draw(rectangle);
}
public static void fillRectangle(Graphics2D g, int x, int y, int w, int h){
Rectangle2D rectangle = new Rectangle2D.Double(x, y, w, h);
g.fill(rectangle);
}
public static void setColor(Graphics2D g, Color color){
g.setColor(color);
}
public static void setStrokeWidth(Graphics2D g, int w){
int strokeWidth = w;
g.setStroke(new BasicStroke(strokeWidth, BasicStroke.CAP_ROUND, BasicStroke.JOIN_ROUND));
}
public static void pause(int t) {
try {
Thread.sleep(t);
}
catch (InterruptedException e) {
System.out.println("Error sleeping");
}
}
public static void putImage(Graphics2D g, int x, int y, String imageURL){
ImageIcon icon = new ImageIcon(imageURL);
Image image = icon.getImage();
g.drawImage(image, x, y, null);
}
public static void drawText(Graphics2D g, String text, int centerx, int centery){
if(text == null)
throw new IllegalArgumentException("Text is null in drawText function!");
FontMetrics metrics = g.getFontMetrics();
int w = metrics.stringWidth(text);
int h = metrics.getDescent();
g.drawString(text, centerx - w/2, centery + h);
}
}
import java.awt.*;
import java.util.LinkedList;
import javax.swing.*;
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){
if(sceneWidth != sceneHeight)
throw new IllegalArgumentException("This demo must be run in a square window!");
this.N = N;
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 ++){
if( i % 100 == 0) {
frame.render(data);
AlgoVisHelper.pause(DELAY);
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 = 200000;
AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight, N);
}
}
import java.awt.*;
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;
}
}
import java.util.LinkedList;
import java.awt.*;
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);
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;
}
}
首先隨機生成20000個點，截圖如下：
在再後面添個0，如下：
由於電腦問題，跑了將近1分鐘，電量警告了。兩次對比，精度提高了。
凌晨1點了，該洗洗睡了。明日再戰......