Triomino问题，即用一个L形的瓦片（有三个小正方形组成）覆盖一个缺少了一个方块（可以是棋盘上的 任何位置）的2^n X 2^n棋盘

Triomino问题的动态演示程序。

源代码：

/**
* 此程序用于解决的问题是：用一个L形的瓦片（有三个小正方形组成）覆盖一个缺少了一个方块（可以是棋盘上的
* 任何位置）的2^n X 2^n棋盘
*/
import javax.swing.*;
import java.awt.*;
import java.applet.*;
import java.awt.geom.*;
import java.awt.event.*;

public class Triomino extends JApplet implements ActionListener , Runnable
{
 private JLabel lx;
 private JLabel ly;
 private JTextField tx;
 private JTextField ty;
 private JButton begin;
 private JButton stop;
 private Image image0;
 private Image image1;
 private Thread demo;
 private int x,y;

 int chessBoard[][] = new int [9][9];//定义一个8 x 8的棋盘
 //private int x,y;

 public void init()
 {
  for(int i=0; i<9; i++)
   for(int j=0; j<9; j++)
   chessBoard[i][j] = 0;
  Container content = getContentPane();
  content.setLayout(new BorderLayout());
  JPanel cotrlPane = new JPanel();
  cotrlPane.setLayout(new FlowLayout());
  //setLayout(null);
  lx = new JLabel("x:");
  cotrlPane.add(lx);
  tx = new JTextField(10);
  cotrlPane.add(tx);
  ly = new JLabel("y:");
  cotrlPane.add(ly);
  ty = new JTextField(10);
  cotrlPane.add(ty);
  begin = new JButton("开始");
  begin.addActionListener(this);
  cotrlPane.add(begin);

  stop = new JButton("清除");
  stop.addActionListener(this);
  cotrlPane.add(stop);

  content.add(cotrlPane, BorderLayout.SOUTH);
  
 }
 /**
 * 0:表示用蓝色方块覆盖棋盘
 * 1:表示用红色方块覆盖棋盘
 * 2:表示用绿色方块覆盖棋盘
 * 3:表示用黑色方块覆盖棋盘，棋盘上被标记为黄色的方块，表示棋盘被分为四部分以后，最中间的四个方块
 *   中，将其中三个所在的部分不包含缺少方块的方块，标记为黑色
 * 4:表示用黄色方块覆盖棋盘，棋盘上被标记为黄色的方块，表示缺少的那个方块
 */
 public void paint(Graphics g)
 {
  Graphics2D g2D = (Graphics2D)g;
  Rectangle2D.Float rectangle;
  
  for(int i=1; i<=8; i++)
   for(int j =1; j<=8; j++)
   {
    switch(chessBoard[i][j])
    {
     case 0:
     {
      g2D.setPaint(Color.blue);
      break;
     }
     case 1:
     {
      g2D.setPaint(Color.red);
      break;
     }
     case 2:
     {
      g2D.setPaint(Color.green);
      break;
     }
     case 3:
     {
      g2D.setPaint(Color.black);
      break;
     }
     case 4:
     {
      g2D.setPaint(Color.yellow);
      break;
     }
     default:break;
    }
    //g2D.setPaint(Color.blue);
    rectangle = new Rectangle2D.Float(10.0f+18*j, 40.0f+18*i, 15.0f, 15.0f);
    //g2D.draw(rectangle);
    //g2D.setPaint(Color.red);
    g2D.fill(rectangle);
   }
  /*int x = 10+18*(int)(7*Math.random());
  int y = 40+18*(int)(7*Math.random());
  g2D.setPaint(Color.red);
  g2D.fill(new Rectangle2D.Float(x,y, 15.0f, 15.0f));*/
  lx.repaint();
  ly.repaint();
  tx.repaint();
  ty.repaint();
  begin.repaint();
  stop.repaint();
 }

 public void actionPerformed(ActionEvent e)
 {
  String action = e.getActionCommand();
  if(action.equals("开始"))
  {
    x = Integer.parseInt(tx.getText());
    y = Integer.parseInt(ty.getText());
   chessBoard[x][y] = 4;
   repaint();
   fillRect(x, y, Color.yellow);
   //trio(x, y, 1, 8, 1, 8);
   if(demo == null || !demo.isAlive())
   {
    demo = new Thread(this);
    demo.start();
   }

  }
  if(action.equals("清除"))
  {
   for(int i=0; i<9; i++)
    for(int j=0; j<9; j++)
     chessBoard[i][j] = 0;
   repaint();
   tx.setText("");
   ty.setText("");
   if(demo != null || demo.isAlive())
    demo = null;
   
   //setDefaultCloseOperation(EXIT_ON_CLOSE);
  }
 }
 /**
 *用分治法解triomino问题
 */
 public void trio(int x, int y, int cStart, int cEnd, int rStart, int rEnd)
 {
  if(cEnd - cStart > 1)
  {
   if(x>=cStart && x<=(cEnd+cStart)/2 && y>=rStart && y<=(rEnd+rStart)/2)
   {
    trio(x, y, cStart, (cEnd+cStart)/2, rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2, (cEnd+cStart)/2+1, cEnd,
     rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, (cEnd+cStart)/2+1, cEnd,
     (rEnd+rStart)/2+1,  rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2+1, cStart, (cEnd+cStart)/2,
     (rEnd+rStart)/2+1,  rEnd);

    /*fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.black);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.black);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1, Color.black);*/
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 3;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 3;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 3;
    pause();
    repaint();

   }
   if(x<=cEnd && x>(cEnd+cStart)/2 && y>=rStart && y<=(rEnd+rStart)/2)
   {
    trio(x, y, (cEnd+cStart)/2+1, cEnd, rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, (cEnd+cStart)/2+1, cEnd,
     (rEnd+rStart)/2+1,  rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2+1, cStart, (cEnd+cStart)/2,
     (rEnd+rStart)/2+1,  rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2, cStart, (cEnd+cStart)/2,
     rStart,  (rEnd+rStart)/2);
    
    /*fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.black);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1,Color.black);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.black);*/
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 3;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 3;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 3;
    pause();
    repaint();

   }
   if(x<=cEnd && x>(cEnd+cStart)/2 && y<=rEnd && y>(rEnd+rStart)/2)
   {
    trio(x, y, (cEnd+cStart)/2+1, cEnd, (rEnd+rStart)/2+1, rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2+1, cStart, (cEnd+cStart)/2,
     (rEnd+rStart)/2+1,  rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2, cStart, (cEnd+cStart)/2,
     rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2, (cEnd+cStart)/2+1, cEnd,
     rStart,  (rEnd+rStart)/2);

    /*fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1, Color.black);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.black);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.black);*/
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 3;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 3;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 3;
    pause();
    repaint();

   }
   if(x>=cStart && x<=(cEnd+cStart)/2 && y<=rEnd && y>(rEnd+rStart)/2)
   {
    trio(x, y, cStart, (cEnd+cStart)/2, (rEnd+rStart)/2+1, rEnd);
    trio((cEnd+cStart)/2, (rEnd+rStart)/2, cStart, (cEnd+cStart)/2,
     rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2, (cEnd+cStart)/2+1, cEnd,
     rStart,  (rEnd+rStart)/2);
    trio((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, (cEnd+cStart)/2+1, cEnd,
     (rEnd+rStart)/2+1,  rEnd);
    
    /*fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.black);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.black);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.black);*/
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 3;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 3;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 3;
    pause();
    repaint();

   }
  }
  else
  {
   if(x>=cStart && x<=(cEnd+cStart)/2 && y>=rStart && y<=(rEnd+rStart)/2)
   {
    /*fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.red);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.red);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1, Color.red);*/
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 1;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 1;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 1;
    pause();
    repaint();
   
   
   }
   if(x<=cEnd && x>(cEnd+cStart)/2 && y>=rStart && y<=(rEnd+rStart)/2)
   {
    /*fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.green);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1,Color.green);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.green);*/
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 2;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 2;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 2;
    pause();
    repaint();
    
   }
   if(x<=cEnd && x>(cEnd+cStart)/2 && y<=rEnd && y>(rEnd+rStart)/2)
   {
    /*fillRect((cEnd+cStart)/2, (rEnd+rStart)/2+1, Color.red);
    fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.red);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.red);*/
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2+1] = 1;
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 1;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 1;
    pause();
    repaint();
    
   } 
   if(x>=cStart && x<=(cEnd+cStart)/2 && y<=rEnd && y>(rEnd+rStart)/2)
   {
    /*fillRect((cEnd+cStart)/2, (rEnd+rStart)/2, Color.green);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2, Color.green);
    fillRect((cEnd+cStart)/2+1, (rEnd+rStart)/2+1, Color.green);*/
    chessBoard[(cEnd+cStart)/2][(rEnd+rStart)/2] = 2;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2] = 2;
    chessBoard[(cEnd+cStart)/2+1][(rEnd+rStart)/2+1] = 2;
    pause();
    repaint();
    
   } 
  }
 }  
 public void run()
 {
  trio(x, y, 1, 8, 1, 8);
 }
 public void pause()
 {
  try
  {
   Thread.sleep(1000);
  } catch (InterruptedException e){}
 }
 public void fillRect(int x, int y, Color color)
 {
  Graphics2D g2D = (Graphics2D)getGraphics();
  g2D.setPaint(color);
  g2D.fill(new Rectangle2D.Float(10.0f+18*x, 40.0f+18*y, 15.0f, 15.0f));
 }   
}