Knight's Tour 递归算法

Question

好的，大家，我知道骑士之旅问题对于所有计算机学生来说都很受欢迎，但我在让我的问题工作时遇到了困难。我使用这种递归算法来完成移动，但是，一旦我到达移动 50 左右，我就必须回溯，因为没有可用的移动，并且我最终永远无法完成游览。我传递一个 ChessNode （保存节点是否已被访问、移动是否被访问等信息）、下一行、下一列和前一个节点的移动计数。

private int moveRecur(ChessNode current, int row, int column, int moveV){
    current.moveVisited = moveV+1;
    if(current.moveVisited > 63){
        return 0;
    }
        if(current.position==13 && aboard[row-1][column+2].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row-1][column+2], row-1, column+2, current.moveVisited);
        }
        else if(current.position==22 && aboard[row-2][column+1].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row-2][column+1], row-2, column+1, current.moveVisited);
        }
        else if(current.position == 50 && aboard[row+1][column-2].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row+1][column-2], row+1, column-2, current.moveVisited);
        }
        else if(current.position == 41 && aboard[row+2][column-1].visited != 1){
            current.visited =1;
            moveRecur(aboard[row+2][column-1], row+2, column-1, current.moveVisited);
        }
        else if(current.position == 46 && aboard[row+2][column+1].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row+2][column+1], row+2, column+1, current.moveVisited);
        }
        else if(current.position == 53 && aboard[row+1][column+2].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row+1][column+2], row+1, column+2, current.moveVisited);
        }
        else if(current.position == 10 && aboard[row-1][column-2].visited != 1){
            current.visited = 1;
            moveRecur(aboard[row-1][column-2], row-1, column-2, current.moveVisited);
        }
        else if (current.position == 17 && aboard[row-2][column-1].visited != 1){
            current.visited =1;
            moveRecur(aboard[row-2][column-1], row-2, column-2, current.moveVisited);
        }
        if(row+1>=0 && row+1<8 && column+2>=0 && column+2<8){
            if(aboard[row+1][column+2].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row+1][column+2], row+1, column+2, current.moveVisited);
            }
        }
        if(row+2>=0 && row+2<8 && column+1>=0 && column+1<8){
            if(aboard[row+2][column+1].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row+2][column+1], row+2, column+1, current.moveVisited);
            }
        }
        if(row-1>=0 && row-1<8 && column-2>=0 && column-2<8){
            if(aboard[row-1][column-2].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row-1][column-2], row-1, column-2, current.moveVisited);
            }
        }
        if(row-2>=0 && row-2<8 && column-1>=0 && column-1<8){
            if(aboard[row-2][column-1].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row-2][column-1], row-2, column-1, current.moveVisited);
            }
        }
        if(row+1>=0 && row+1<8 && column-2>=0 && column-2<8){
            if(aboard[row+1][column-2].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row+1][column-2], row+1, column-2, current.moveVisited);
            }
        }
        if(row+2>=0 && row+2<8 && column-1>=0 && column-1<8){
            if(aboard[row+2][column-1].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row+2][column-1], row+2, column-1, current.moveVisited);
            }
        }
        if(row-1>=0 && row-1<8 && column+2>=0 && column+2<8){
            if(aboard[row-1][column+2].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row-1][column+2], row-1, column+2, current.moveVisited);
            }
        }
        if(row-2>=0 && row-2<8 && column+1>=0 && column+1<8){
            if(aboard[row-2][column+1].visited != 1){
                current.visited = 1;
                moveRecur(aboard[row-2][column+1], row-2, column+1, current.moveVisited);
            }
        }
    //System.out.println(current.position + " "+current.moveVisited);
    current.visited = 0;    
    return 0;
}

因此，最初我检查可以移动到角板位置的点，然后我只是根据可用的移动进行递归调用。所以我想我的主要问题是我做错了什么吗？或者我可以使用其他条件来使旅行更加直观吗？

提前致谢！

Answer 1

这是java中的骑士之旅代码，布局非常精彩。我使用递归回溯来完成此操作。这是我的课堂作业。如果您在理解或运行此代码时遇到任何问题，请与我联系。

package knights.tour;
import java.awt.*;
import java.awt.event.*;
import java.util.logging.*;
import javax.swing.*;


public class KnightsTour extends JFrame implements ActionListener{

//All the static variables used between action listeners and functions.
public static String path;
public static int btnPressed = 0;
public static int rowSelected;
public static String[] pathArray;
public static int[][] coordinatesArray;
public static int columnSelected;  
public static int flag =0;
public static int increment = 0;
public static JPanel panel1 = new JPanel();
public static JPanel panel3 ;
public static JButton btnStart = new JButton("Start Animation");
public static JButton btnClear = new JButton("Clear");
public static JTextArea lblPath = new JTextArea();
public static JLabel lblStartRow = new JLabel();
public static JLabel lblStartColumn = new JLabel();
public static JButton[][] button;
public static int variableForIncrement=0;
static int row ;
static int column ;
static int[][] array = new int[row][column];
public static int count = 1;


KnightsTour(){

    //Setting layout of the frame in the constructor and adding buttons to the panel and the frame.
     getContentPane().setLayout(new GridLayout(2,1));
    lblPath.setLineWrap(true);
    lblPath.setColumns(10);
    lblPath.setSize(700, 100);
    lblPath.setEditable(false);
    panel1.add(btnStart);
    panel1.add(btnClear);
    panel1.add(lblStartRow);
    panel1.add(lblStartColumn);
    panel1.add(lblPath);
    panel3 = new JPanel(new GridLayout(row,column));

    // Initializing Array of buttons for the user to click on the chess board.
    button= new JButton[row][column];
     array = new int[row][column];
     coordinatesArray = new int[row*column][2];  // This array stores the coordinates as the Knight                            
    for(int i=0;i<row;i++){
        for(int j=0;j<column;j++){
            button[i][j]  = new JButton();
        }
    }

    //Setting background of the buttons to black and white for chessboard layout.
     for(int i=0;i<row;i++){
        for(int j=0;j<column;j++){
            if(i%2 ==j%2){
                button[i][j].setBackground(Color.BLACK);
                button[i][j].setForeground(Color.WHITE);
        }
            else{
                button[i][j].setBackground(Color.WHITE);
            }
            panel3.add(button[i][j]);
            button[i][j].addActionListener(this);
        }
   }

     btnClear.addActionListener(this);
     btnStart.addActionListener(this);
     add(panel3);
     add(panel1); 
   setDefaultCloseOperation(EXIT_ON_CLOSE);

}

public static void main(String[] args) {
  // TODO code application logic here
    String input =JOptionPane.showInputDialog("Enter the rows and columns in the format             (row,column)");
    String[] ar = input.split(",");
    row = Integer.parseInt(ar[0]);   // Finding out row and column from the user input.
    column = Integer.parseInt(ar[1]);
    pathArray = new String[row*column];  // This array is kept to store the path of the knight.
    JFrame frame = new KnightsTour();    
   frame.setVisible(true);
   frame.setSize(700,700);

}


//All the computation takes place in this function. It checks the neighbour and recursively calls itself.
public static void neighbourRecursion(int a,int b){

    pathArray[increment] = Integer.toString(a) + "," + Integer.toString(b);  // Storing the path of the Knight
    increment++;
    array[a][b] = count;                                                     //Stroing value of count.
    button[a][b].setText(String.valueOf(count));
    coordinatesArray[variableForIncrement][0] = button[a][b].getX();         //Finding coordinates of buttons to show animation
    coordinatesArray[variableForIncrement][1] = button[a][b].getY();
    count++;
    variableForIncrement++;

    //Checking for valid neighbours and calling itself recursively.
    if(a <= row-3 && b<=column-2){
        if(alreadyVisited(a+2,b+1)){
        neighbourRecursion(a+2,b+1);
        }
    }
     if(a<=row-3 && b>=1){
        if(alreadyVisited(a+2,b-1)){
        neighbourRecursion(a+2,b-1);
    }
    }
     if(a>=2 && b<=column-2){
        if(alreadyVisited(a-2,b+1)){
        neighbourRecursion(a-2,b+1);
    }
    }

     if(a>=2 && b>=1){
        if(alreadyVisited(a-2,b-1)){

        neighbourRecursion(a-2,b-1);
    }

    }
     if(a<=row-2 && b>=2){
        if(alreadyVisited(a+1,b-2)){

        neighbourRecursion(a+1,b-2);
    }
    }

     if(a<=row-2 && b<=column-3){
        if(alreadyVisited(a+1,b+2)){

        neighbourRecursion(a+1,b+2);
    }
    }
     if(a>=1 && b>=2){
        if(alreadyVisited(a-1,b-2)){
        neighbourRecursion(a-1,b-2);
    }
    }
     if(a>=1 && b <=column-3){
        if(alreadyVisited(a-1,b+2)){
        neighbourRecursion(a-1,b+2);
    }
    }


     //Breaking condition of the function.
     if(count == (row*column)+1){
     }


     // Backtracking condition if there is no neighbour.
    else{
         button[a][b].setText(""); 
        array[a][b]=0;
         count--;
         variableForIncrement--;
         if(increment >0){
         increment--;
         }
         return ;

    }


}
 //This function checks if the neighbour is already visited.
public static boolean alreadyVisited(int a,int b){

if(array[a][b] != 0){
    return false;
}
else{
    return true;
}
}

@Override
public void actionPerformed(ActionEvent e) {
    //when clear is pressed all arrays  and global variables are set to initial conditon.
if(e.getSource() == btnClear){
        for(int i =0;i<row;i++){
            for(int j=0;j<column;j++){
                array[i][j] = 0;
                button[i][j].setText("");
                count = 1;
                lblPath.setText("");
                lblStartRow.setText("");
                lblStartColumn.setText("");
                flag =0;
                variableForIncrement=0;
                increment =0;
                path ="    ";

    }
        }

      }

 //If start animation button is pressed animation is started.
      else if(e.getSource() == btnStart){
          animate();
      }

      // When the button is pressed. 

      else{
        for(int i=0;i<row;i++){
        for(int j=0;j<column;j++){
        if(e.getSource() == button[i][j]){
            if(flag == 1){
                lblPath.setText("  Please press clear before clicking again");   // Button pressed      twice without reset.
            }
            else{
       rowSelected = i;
       columnSelected =j;
       // If odd * odd board and selected postion is odd then No path is possible.
       if(row%2 ==1 && column%2 == 1 && rowSelected%2 ==0 && columnSelected%2 == 1 || row%2 ==1 &&     column%2 == 1 && rowSelected%2 ==1 && columnSelected%2 == 0){
           lblPath.setText("   Path not possible from this point");
       }
       else{
           int count;
       lblStartRow.setText("Starting Row : "+String.valueOf(rowSelected + 1));
       lblStartColumn.setText("Starting Column : "+String.valueOf(columnSelected + 1));
       count = 1; 
       flag = 1;
       startTour();    //Start tour function called.
       for(int q=0;q<row;q++){
           for(int w=0;w<column;w++){
               if(array[i][j] == 0){
                   count++;
               }
           }

       }
       if(count > 2){
           lblPath.setText("   No Path found");
       }

       //Printing path of the knight here.
       else{
       for(int k=0;k<pathArray.length;k++){
           path = path+"->"+ pathArray[k];
       }
       lblPath.setText("   Path : \n"+ path.substring(5));   
       }
        btnPressed = 1;
        break;
   }

            }
        }

   }



 }
 }    }


//Function for the animation. 
 void animate(){
     if(btnPressed == 1){
     btnPressed =0;
    Graphics g = getGraphics();
    for(int i=0;i<(row*column)-1;i++){
     try {
         Thread.sleep(600);   // this function slows down drawing of lines.

     } catch (InterruptedException ex) {

     }
           g.setColor(Color.RED);   // setting colour or line to red.
          g.drawLine((coordinatesArray[i][0]+65),(coordinatesArray[i][1]+50),(coordinatesArray[i+1]   [0]+65),(coordinatesArray[i+1][1]+50));
    }
     }
    else{
         lblPath.setText("  Please clear, select a button to see the animation again");  //Animate    button pressed twice without clear.
     }

}

 //This function calls the neighbour function with the selected row and column by the user.
  static void startTour(){
         neighbourRecursion(rowSelected,columnSelected);
    for(int i=0;i<row;i++){
        for(int j=0;j<column;j++){
            System.out.print(array[i][j]+" ");
        }
        System.out.println();
    }
   }

 }

Answer 2

我用 C# 实现了这个程序。您可以在这里找到它：

http://github.com/danieltian/KnightBoard

它只会找到第一个解决方案。我并不是说要复制它，但你可以看一下它是否有帮助。