关于100个人随机给钱的模拟实验

前言

在知乎上看到一个好玩的问题：房间里有100个人，每人都有100元钱，他们在玩一个游戏。每轮游戏中，每个人都要拿出一元钱随机给另一个人，最后这100个人的财富分布是怎样的？

今天使用java中的GUI来模拟一下。

实现

效果图如下

红色表示负债，模拟次数大概150W次。

代码实现

可视化主类

import java.awt.EventQueue;
import java.util.Arrays;

public class AlgoVisualizer {

  private static int DELAY = 40;
  private int[] money;
  private AlgoFrame frame;

  public AlgoVisualizer(int sceneWidth, int sceneHeight) {

    // 初始化数据
    money = new int[100];
    for (int i = 0; i < money.length; i++) {
      money[i] = 100;
    }

    // 初始化视图
    EventQueue.invokeLater(() -> {
      frame = new AlgoFrame("Money Problem", sceneWidth, sceneHeight);
      new Thread(this::run).start();
    });
  }

  public void run() {

    while (true) {

      // 改进2：是否排序
      Arrays.sort(money);
      frame.render(money);
      AlgoVisHelper.pause(DELAY);

      // 改进1：每一帧执行的轮数
      for (int k = 0; k < 50; k++) {
        for (int i = 0; i < money.length; i++) {
          // 改进3：允许money为负值
          //if(money[i] > 0){
          int j = (int) (Math.random() * money.length);
          money[i] -= 1;
          money[j] += 1;
          //}
        }
      }
    }
  }

  public static void main(String[] args) {

    int sceneWidth = 1000;
    int sceneHeight = 800;

    AlgoVisualizer vis = new AlgoVisualizer(sceneWidth, sceneHeight);
  }
}

窗口类

import java.awt.Dimension;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.RenderingHints;
import javax.swing.JFrame;
import javax.swing.JPanel;

/**
 * 主窗口
 */
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 int[] money;

  public void render(int[] money) {
    this.money = money;
    repaint();
  }

  private class AlgoCanvas extends JPanel {

    public AlgoCanvas() {
      // 双缓存
      super(true);
    }

    @Override
    public void paintComponent(Graphics g) {
      super.paintComponent(g);

      Graphics2D g2d = (Graphics2D) g;

      // 抗锯齿
      RenderingHints hints = new RenderingHints(
          RenderingHints.KEY_ANTIALIASING,
          RenderingHints.VALUE_ANTIALIAS_ON);
      hints.put(RenderingHints.KEY_RENDERING, RenderingHints.VALUE_RENDER_QUALITY);
      g2d.addRenderingHints(hints);

      // 具体绘制
      int w = canvasWidth / money.length;
      for (int i = 0; i < money.length; i++) {
        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]);
        }
      }
    }

    @Override
    public Dimension getPreferredSize() {
      return new Dimension(canvasWidth, canvasHeight);
    }
  }
}

工具类

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;

/**
 * 工具类
 */
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);
  }

}

参考

该如何面对这个残酷的世界？-搜狐财经
关于“房间里有100个人，每人都有100元钱，每轮每人要拿一元钱随机给另一个人”这个游戏的解析解。-知乎
关于100个人随机给钱的模拟实验。-知乎