看的見得算法第三章概率模擬算法

1.一個有意思的分錢模擬問題

AlgoFrame.java中

在render方法中設置數據

  // TODO: 設置自己的數據
    int[] money;
    public void render(int[] money){
        this.money = money;
        repaint();
    }

繪製方法paintComponent中

int w = canvasWidth / money.length;//每一個小矩形的寬度
            for(int i = 0 ; i < money.length ; i ++)//左上角XY座標，寬度，高
                AlgoVisHelper.fillRectangle(g2d,
                        i*w+1, canvasHeight-money[i], w-1, money[i]);

AlgoVisualize.java

設置初始每個人100元

        // TODO: 初始化數據
        money = new int[100];
        for(int i = 0; i < money.length; i++){
            money[i] = 100;
        }

每一輪第i個人給隨機一個人1塊錢

 // 動畫邏輯
    private void run(){
        while(true) {
            // TODO: 編寫自己的動畫邏輯
            frame.render(money);
            AlgoVisHelper.pause(1);
            for (int i = 0; i < money.length; i++) {
                if (money[i] > 0) {
                    int j = (int) (Math.random() * money.length);
                    money[i] -= 1;
                    money[j] += 1;
                }
            }
        }
    }

2.深入隨機分錢問題

加快速度，計算50次後再render顯示。

            for(int k = 0; k< 50; k++){
                for (int i = 0; i < money.length; i++) {
                    if (money[i] > 0) {
                        int j = (int) (Math.random() * money.length);
                        money[i] -= 1;
                        money[j] += 1;
                    }
                }
            }

考慮有人的錢爲負數。

當錢爲正數,x座標不變，y座標爲panel面板高度的1/2減去錢，寬度爲w減去間隔1，高是錢money[i]

當錢爲正數,x座標不變，y座標爲panel面板高度的1/2，寬度爲w減去間隔1，高是錢-money[i]

int w = canvasWidth / money.length;//每一個小矩形的寬度
            for(int i = 0 ; i < money.length ; i ++) {//左上角X，Y座標，寬度，高
                if (money[i] > 0) {
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
                    AlgoVisHelper.fillRectangle(g2d, i * w + 1, canvasHeight / 2 - money[i], w - 1, money[i]);
                }
                else{
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
                    AlgoVisHelper.fillRectangle(g2d, i * w + 1, canvasHeight / 2, w - 1, -money[i]);
                }
            }

3 蒙特卡洛算法隨機模擬

AlgoFrame.java

設置數據

    // TODO: 設置自己的數據
    private Circle circle;
    private LinkedList<Point> points;
    public void render(Circle circle, LinkedList<Point> points){
        this.circle = circle;
        this.points = points;
        repaint();
    }

具體繪製方法paintComponent，先繪製一個圈，圈內的點紅色，圈外綠色，點用實心圓畫。

            // 具體繪製
            // TODO： 繪製自己的數據data
            AlgoVisHelper.setStrokeWidth(g2d,3);
            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
            AlgoVisHelper.strokeCircle(g2d, circle.getX(), circle.getY(), circle.getR());
            for(int i = 0; i < points.size(); i++){
                Point p =points.get(i);
                if(circle.contain(p))
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
                else
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                AlgoVisHelper.fillCircle(g2d, p.x, p.y, 3);
            }

AlgoVisualizer.java

定義變量

    // TODO: 創建自己的數據
    private Circle circle;//圓
    private LinkedList<Point> points;//點隊列
    private AlgoFrame frame;    // 視圖
    private int N;//點個數
    private static int DELAY = 40;//刷新停頓

實例化類方法，傳參爲界面寬高，點的個數。

    public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
        // TODO: 初始化數據
        if(sceneWidth != sceneHeight)
            throw new IllegalArgumentException("This demo must be run in a square window!");
        this.N = N;
        circle = new Circle(sceneWidth/2, sceneHeight/2, sceneWidth/2);
        points = new LinkedList<Point>();
        // 初始化視圖
        EventQueue.invokeLater(() -> {
            frame = new AlgoFrame("Welcome", sceneWidth, sceneHeight);
            new Thread(() -> {
                run();
            }).start();
        });
    }

動畫邏輯方法，點的座標爲(0~1隨機值)*面板的寬高，frame的render方法不斷調用PaintComonent方法刷新控件。

    private void run(){
        for(int i = 0; i < N; i++){
            frame.render(circle, points);//刷新控件
            AlgoVisHelper.pause(DELAY);//停頓
            int x = (int)(Math.random() * frame.getCanvasWidth());
            int y = (int)(Math.random() * frame.getCanvasHeight());
            Point p = new Point(x, y);//點的位置
            points.add(p);
        }
    }

Main方法

    public static void main(String[] args) {
        int sceneWidth = 800;
        int sceneHeight = 800;
        int N = 10000;
        // TODO: 根據需要設置其他參數，初始化visualizer
        AlgoVisualizer visualizer = new AlgoVisualizer(sceneWidth, sceneHeight, N);
    }

4.用蒙特卡洛算法計算π值

MonteCarloPiData.java

數據類，主要包含圓、點列表

import java.util.LinkedList;
import java.awt.*;
public class MonteCarloPiData {
    private Circle circle;//圓
    private LinkedList<Point> points;//點列表
    private int insideCircle = 0;//在圓內的點
    public MonteCarloPiData(Circle circle){//構造函數
        this.circle = circle;
        points = new LinkedList<Point>();
    }
    public Circle getCircle(){
        return circle;
    }//返回圓
    public int getPointsNumber(){
        return points.size();
    }//所有點數目
    public Point getPoint(int i){//獲得第幾個點
        if(i < 0 || i >= points.size())
            throw new IllegalArgumentException("out of bound in getPoint!");
        return points.get(i);
    }
    public void addPoint(Point p){//統計在圈內的點
        points.add(p);
        if(circle.contain(p))
            insideCircle ++;
    }
    public double estimatePi(){//計算π值
        if(points.size() == 0)
            return 0.0;
        int circleArea = insideCircle;
        int squareArea = points.size();
        return (double)circleArea * 4 / squareArea;
    }
}

視圖層AlgoFrame.java

render方法設置數據：

    // TODO: 設置自己的數據
    private MonteCarloPiData data;
    public void render(MonteCarloPiData data){
        this.data = data;
        repaint();
    }

paintComponent繪製方法中具體繪製：

         // TODO： 繪製自己的數據data
            AlgoVisHelper.setStrokeWidth(g2d,3);
            AlgoVisHelper.setColor(g2d, AlgoVisHelper.Blue);
            Circle circle = data.getCircle();//取出圓
            AlgoVisHelper.strokeCircle(g2d, circle.getX(), circle.getY(), circle.getR());
            for(int i = 0; i < data.getPointsNumber(); i++){
                Point p =data.getPoint(i);//取出第i個點
                if(circle.contain(p))
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Red);
                else
                    AlgoVisHelper.setColor(g2d, AlgoVisHelper.Green);
                AlgoVisHelper.fillCircle(g2d, p.x, p.y, 3);
            }

AlgoVisualizer.java

控制層

創建數據

    // TODO: 創建自己的數據
    private MonteCarloPiData data;//數據對象，參數包括圓和點列表
    private AlgoFrame frame;    // 視圖
    private int N;//點個數
    private static int DELAY = 1;//刷新每個點停頓

構造方法初始化數據

    public AlgoVisualizer(int sceneWidth, int sceneHeight, int N){
        // TODO: 初始化數據
        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);
        // 初始化視圖
        EventQueue.invokeLater(() -> {
            frame = new AlgoFrame("Welcome", sceneWidth, sceneHeight);
            new Thread(() -> {
                run();
            }).start();
        });
    }

動畫邏輯run方法

    // 動畫邏輯
    private void run(){
        for(int i = 0; i < N; i++){
            if( i % 100 == 0) {
                frame.render(data);//刷新控件
                AlgoVisHelper.pause(DELAY);//停頓
                System.out.println(data.estimatePi());//輸出π計算值
            }
            int x = (int)(Math.random() * frame.getCanvasWidth());
            int y = (int)(Math.random() * frame.getCanvasHeight());
            data.addPoint(new Point(x, y));
        }
    }

5不用UI計算π：

圓類Circle.java，參數圓心的座標x，y，半徑r，類方法contain判斷點是否在圓內。

算法類MonteCarloPiData.java，參數圓。

測試類MonteCarloExperiment.java，參數正方型邊長squareSide,點個數N。

類方法run先建立MonteCarloPiData對象data，然後隨機模擬點，使用data的方法addPoint加入每個點。每一百次計算π值。

import java.awt.*;
public class MonteCarloExperiment {
    private int squareSide;
    private int N;
    public MonteCarloExperiment(int squareSide, int N){
        if(squareSide <= 0 || N <= 0)
            throw new IllegalArgumentException("squareSide and N must larger than zero!");
        this.squareSide = squareSide;
        this.N = N;
    }
    public void run(){
        Circle circle = new Circle(squareSide/2, squareSide/2, squareSide/2);
        MonteCarloPiData data = new MonteCarloPiData(circle);
        for(int i = 0 ; i < N ; i ++){
            if( i % 100 == 0) {
                System.out.println(data.estimatePi());
            }
            int x = (int)(Math.random() * squareSide);
            int y = (int)(Math.random() * squareSide);
            data.addPoint(new Point(x, y));
        }
    }
}

6、三門問題

public class ThreeGatesExperiment {
    private int N;
    public ThreeGatesExperiment(int N){
        if(N <= 0)
            throw new IllegalArgumentException("N<=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
        int prizeDoor = (int)(Math.random() * 3);
        int playerChoice = (int)(Math.random() * 3);
        if( playerChoice == prizeDoor)
            return changeDoor ? false : true;
        else
            return changeDoor ? true : false;
    }
}

7 抽5次中獎率爲20%的獎品。

public class WinningPrize {
    private double chance;//一次中獎的概率0.2
    private int playTime;//開幾次寶箱5
    private int N;//模擬幾次
    public WinningPrize(double chance, int playTime, int N){
        if(chance < 0.0 || chance > 1.0)
            throw new IllegalArgumentException("chance must be between 0 and 1!");
        if(playTime <= 0 || N <= 0)
            throw new IllegalArgumentException("playTime or N must be larger than 0!");
        this.chance = chance;
        this.playTime = playTime;
        this.N = N;
    }
    public void run(){
        int wins = 0;
        for(int i = 0 ; i < N ; i ++)
            if(play())
                wins ++;
        System.out.println("winning rate: " + (double)wins/N);
    }
    private boolean play(){
        for(int i = 0 ; i < playTime ; i ++)
            if(Math.random() < chance)//0-1之間的數，小於chance就中獎
                return true;
        return false;
    }
}

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看的見得算法 第三章 概率模擬算法

看的見得算法第三章概率模擬算法