问题
I'm currently studying my second programming course in java and have a problem with an assignment that I need to complete to pass the course. Basically it's about writing a program that recursively solves sudoku with backtracking. This is the algorithm I came up with. I used a 9x9 array to represent the grid which in the beginning is filled with zeroes. checkFill checks whether it's possible to insert a number (var) into a position[i][j]. The problem is that it only solves sudoku partially it always returns false(no solution) and some cells still contain zeroes. What am I doing wrong here?
import java.awt.*;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;
import javax.swing.*;
public class Sudoku {
private int[][] sudoku;
private JFrame frame;
private JFormattedTextField[][] sudokuSquares;
private JButton solve, clear;
public Sudoku() {
sudoku = new int[9][9];
frame = new JFrame("Sudoku Solver");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
JPanel northPanel = new JPanel();
northPanel.setLayout(new GridLayout(9, 9));
northPanel.setBorder(BorderFactory.createEmptyBorder(10, 10, 10, 10));
sudokuSquares = new JFormattedTextField[9][9];
Font font1 = new Font("SansSerif", Font.BOLD, 20);
for(int i = 0; i < 9; i++) {
for(int j = 0; j < 9; j++) {
sudokuSquares[i][j] = new JFormattedTextField();
sudokuSquares[i][j].setHorizontalAlignment(JTextField.CENTER);
sudokuSquares[i][j].setFont(font1);
sudokuSquares[i][j].setBorder(BorderFactory.createEtchedBorder(javax.swing.border.EtchedBorder.RAISED));
northPanel.add(sudokuSquares[i][j]);
}
}
setColor();
frame.add(northPanel, BorderLayout.NORTH);
JPanel southPanel = new JPanel();
solve = new JButton("Solve");
solve.addActionListener(new SolveButtonListener());
clear = new JButton("Clear");
clear.addActionListener(new ClearButtonListener());
southPanel.add(clear);
southPanel.add(solve);
frame.add(southPanel, BorderLayout.SOUTH);
frame.setResizable(false);
frame.setSize(280, 330);
frame.setVisible(true);
}
private void solveSudoku() {
boolean hasSolution = solve(0, 0);
if(hasSolution) {
JOptionPane.showMessageDialog(frame, "Sudoku has been successfully solved");
} else {
JOptionPane.showMessageDialog(frame, "Sudoku has no solution");
}
}
private class SolveButtonListener implements ActionListener {
@Override
/**
* Checks input for errors and outputs the sudoku matrix after it's been solved.
*/
public void actionPerformed(ActionEvent e) {
String s;
setColor();
for(int i = 0; i < 9; i++) {
for(int j = 0; j < 9; j++) {
s = sudokuSquares[i][j].getText();
if(s.isEmpty()) {
s = "0";
} else if(s.length() > 1 || !Character.isDigit(s.charAt(0)) || s.charAt(0) == '0') {
sudokuSquares[i][j].setBackground(Color.RED);
JOptionPane.showMessageDialog(frame, "Invalid entry! Please enter a number between 1-9");
return;
}
sudoku[i][j] = Integer.parseInt(s);
}
}
solveSudoku();
for(int i = 0; i < 9; i++) {
for(int j = 0; j < 9; j++) {
sudokuSquares[i][j].setText(String.valueOf(sudoku[i][j]));
}
}
}
}
private class ClearButtonListener implements ActionListener {
@Override
public void actionPerformed(ActionEvent e) {
for(int i = 0; i < 9; i++) {
for(int j = 0; j < 9; j++) {
sudokuSquares[i][j].setText("");
}
}
setColor();
}
}
/**
* Sets the background color of sudoku cells
*/
private void setColor() {
for(int i = 0; i < 9; i++) {
for(int j = 0; j < 9; j++) {
if((i / 3 < 1 || i / 3 >= 2) && (j / 3 < 1 || j / 3 >= 2) ||
(i / 3 >= 1 && i / 3 < 2) && (j / 3 >= 1 && j / 3 < 2)) {
sudokuSquares[i][j].setBackground(new Color(220, 220, 220));
} else {
sudokuSquares[i][j].setBackground(Color.WHITE);
}
}
}
}
/**
* Solves the sudoku through recursive technique
* @param i row
* @param j column
* @return returns true if the sudoku has a solution, returns false otherwise
*/
private boolean solve(int i, int j) {
if(i > 8) {
return true;
}
if(sudoku[i][j] == 0) {
for(int var = 1; var < 10; var++) {
if(checkFill(i, j, var)) {
sudoku[i][j] = var;
if(j >= 8) {
solve(i + 1, 0);
} else {
solve(i, j+1);
}
}
}
} else {
if(j >= 8) {
solve(i + 1, 0);
} else {
solve(i, j+1);
}
}
return false;
}
/**
* Checks if var could be inserted at position [i][j]
* @param i row
* @param j column
* @param var number to be checked for possible insertion
* @return
*/
private boolean checkFill(int i, int j, int var) {
for(int a = 0; a < 9; a++) {
if(sudoku[a][j] == var) {
return false;
}
}
for(int a = 0; a < 9; a++) {
if(sudoku[i][a] == var) {
return false;
}
}
int tempI = (i / 3) * 3;
int tempJ = (j / 3) * 3;
for(int a = 0; a < 3; a++) {
for(int b = 0; b < 3; b++) {
if(sudoku[tempI + a][tempJ + b] == var)
return false;
}
}
return true;
}
}
So anyone got any ideas?
回答1:
It seems that your program simply checks if a given number can fit into a given slot, checks the row, column, and local 3x3 grid, and places it there permanently if those three checks pass.
This is problematic since most sudoku will not yield a single possibility on such simple checks.
You'll need to make a list of possible values for each spot, then start using techniques such as double pairs to solve it out further.
Since it's a computer and it's fast, after you use some of these techniques you can start brute forcing it.
A different approach would be to translate the sudoku problem into a SAT formula, feed it into a SAT solver, and translate the solution back into a sudoku solution. There are very advanced SAT solvers these days that can handle 9x9 sudoku very quickly. Here is a more in-depth explanation.
回答2:
In your solve method, you test whether sudoku[i][j]==0 before you make a change. That means that once you place a number, whether it's right or wrong, you never change it. You need to be able to back out of errant moves.
回答3:
You can find a simplified java Sudoku program here.http://www.heimetli.ch/ffh/simplifiedsudoku.html
if you can share you full source code including the method checkFill, we can assist you in debuging further
来源：https://stackoverflow.com/questions/15332134/recursive-method-for-solving-sudoku