骑士之旅回溯

Question

我正在研究骑士的旅行问题，并使用回溯算法。 我的代码最后没有产生正确的输出，只是一遍又一遍地重复最后两个条目，直到没有达到n ^ 2 -1为止。

这是我的代码。 我正在遵循此伪代码http://www.wou.edu/~broegb/Cs345/KnightTour.pdf

visited = [[False for x in range(5)] for y in range(5)]

def move(x,y,m):

    result=False
    if x<0 or x>=5 or y<0 or y>=5:
        return False
    if visited[x][y]==True:
        return False
    if m==24:
        print "a solution has been found"
        print x,",",y


        visited[x][y]=True
        return True

    else:
        result=result or move(x+2,y+1,m+1)
        result=result or  move(x+2,y-1,m+1)
        result=result or move(x-2,y+1,m+1)
        result=result or move(x-2,y-1,m+1)
        result=result or move(x+1,y+1,m+1)
        result=result or move(x+1,y-1,m+1)
        result=result or move(x-1,y+1,m+1)
        result=result or move(x-1,y-1,m+1)
    if result==True:
        print x,",",y

        return True
    else:
        visited[x][y]=False
        return False

Answer 1

您正在visited[x][y]=True的设置为visited[x][y]=True在算法结束时为true。 您必须在其中将其分类后再进行设置。 我还对您的代码进行了一些增强：

N = 5 # This way you can test it with 5 or 6 and even 100 if you want to.
visited = [[False for x in range(N)] for y in range(N)]

def move(x,y,m):

    result=False
    if x<0 or x>=N or y<0 or y>=N or visited[x][y]==True: # You may merge these two ifs.
        return False
    visited[x][y]=True
    if m==(N * N - 1):
        print "a solution has been found"
        visited[x][y]=True # Set visited here tot true.
        return True
    else:
        print x,",",y
        if (move(x+2,y+1,m+1) or move(x+2,y-1,m+1)
            or move(x-2,y+1,m+1) or move(x-2,y-1,m+1)
            or move(x+1,y+1,m+1) or move(x+1,y-1,m+1)
            or move(x-1,y+1,m+1) or move(x-1,y-1,m+1)): # Place them in one if.
            print x,",",y

            return True
    return False # If the algorithm comes here it may return false

print move(2,1,0)

Answer 2

您似乎在下半步中犯了一个错误。 您要在y中加1或从y中减去1，而应为2。因此，完整的移动集如下所示：

    result=result or move(x+2,y+1,m+1)
    result=result or move(x+2,y-1,m+1)
    result=result or move(x-2,y+1,m+1)
    result=result or move(x-2,y-1,m+1)
    result=result or move(x+1,y+2,m+1)
    result=result or move(x+1,y-2,m+1)
    result=result or move(x-1,y+2,m+1)
    result=result or move(x-1,y-2,m+1)

Answer 3

您要实现的伪代码算法有错误。 在递归的情况下，您永远不会将任何visited值都设置为True 。

在执行任何递归调用之前，请尝试将visited[x][y]=True的行visited[x][y]=True从if块移至以下else块。 （您也可以只复制它，但实际上它并没有做任何有用的操作。）

Answer 4

这是Java中的Knight巡回代码，具有出色的布局。 我使用递归进行回溯。 这是我的课。 如果您对理解或运行此代码有任何疑问，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();
    }
   }

 }