Probieren geht über Studieren: Backtracking

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public class XYProblem {
 
    gelöst = false;
 
    public löse() {
        löse(0);
    }
 
    private löse(aktuellePosition) {
        if (aktuellePosition > letztePosition) gelöst;
 
        while (Möglichkeit vorhanden) {
            setzen;
            löse(akuellePosition + 1);
        }
        if (ungelöst) zurücksetzen;
    }
}

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import java.io.BufferedReader;
import java.io.File;
import java.io.FileReader;
import java.io.IOException;
import java.util.ArrayList;
import java.util.List;
 
/**
 * 3x3 sudokusolver
 * @author nrg
 */
public class SudokuSolver {
 
    private int[][] sudoku;
    private boolean solved;
 
    /**
     * Constructs a sudokusolver. Note that there is no intialization since yet.
     * You have to read the sudoku from file or use the set-method before
     * invoking the solve-method.
     */
    public SudokuSolver() {
        this.solved = false;
    }
 
    /**
     * Constructs a sudokusolver
     * @param sudoku 2d array represent the soduko, 0 expected for empty fields
     */
    public SudokuSolver(int[][] sudoku) {
        setSudoku(sudoku);
    }
 
    /**
     * Sets sudoku
     * @param sudoku 2d array represent the soduko, 0 expected for empty fields
     */
    public void setSudoku(int[][] sudoku) {
        this.solved = false;
        this.sudoku = sudoku;
    }
 
    /**
     * Returns the current sate of the sudoku
     * @return 2d array represent the soduko
     */
    public int[][] getSudoku() {
        return this.sudoku;
    }
 
    /**
     * Reads a suduko from a file, space as delimiter and point for empty fields are expected
     * 
     * for example
     * 
     * 2 . 7 . 8 6 . . .
     * . 5 . 7 1 . . 8
     * . 9 8 . 4 . 1 7 6
     * . . 4 . . 9 . . 7
     * . 8 . 7 . 5 . 3 .
     * . . . 4 . . 9 2 5
     * 8 . 3 . . . . 5 2
     * 7 . . . 2 . 3 . .
     * . . . 6 5 . . . 1
     * 
     * represents a 3x3 sudoku
     * 
     * @param file the filepath 
     * @throws IOException
     */
    public void read(String file) throws IOException {
        read(new File(file));
    }
 
    /**
     * Reads a suduko from a file, space as delimiter and point for empty fields is expected
     * for example and further details see {@link SudokuSolver#read(String)}
     * @param file the fileobjekt
     * @throws IOException
     */
    public void read(File file) throws IOException {
        BufferedReader bisr = new BufferedReader(new FileReader(file));
        List<String> lines = new ArrayList<String>();
        String line = null;
        while ((line = bisr.readLine()) != null)
            lines.add(line);
        solved = false;
        sudoku = new int[lines.size()][];
        for (int i = 0; i < lines.size(); i++)
            sudoku[i] = parseLine(lines.get(i).split("\\s"));
    }
 
    /**
     * solve the current given sudoku
     * @return the solve-time in nanoseconds
     * @throws IllegalStateException if sudoku == null
     * @throws UnsolveableSudokuException if the sudoko can not be solved
     * @throws InvalidSudokuException if the sudoko is not 3x3
     */
    public long solve() {
        if (sudoku == null) throw new IllegalStateException("initialize sodoku first");
        
        if (sudoku.length != 9)
            throw new InvalidSudokuException("number of rows must be 9");
        for (int i = 0; i < sudoku.length; i++) {
            if (sudoku[i].length != 9)
                throw new InvalidSudokuException("number of columns in row " + (i+1) + " must be 9");
        }
        
        long start = System.nanoTime();
        if (!solved) solve(0, 0);
        if (!solved) throw new UnsolveableSudokuException("sudoku cannot be solved");
        return System.nanoTime() - start;
    }
 
    /**
     * backtracking recursion
     * @param row current row
     * @param col current col
     */
    private void solve(int row, int col) {
        if (solved = row >= sudoku.length) return;
 
        if (sudoku[row][col] == 0) {
            for (int n : getPossibilities(row, col)) {
                if (solved) break;
                sudoku[row][col] = n;
                solve(nextRow(row, col), nextCol(row, col));
            }
            if (!solved) sudoku[row][col] = 0;
        } else {
            solve(nextRow(row, col), nextCol(row, col));
        }
    }
 
    /**
     * returns the next row
     * @param row current row
     * @param col current col
     * @return next row
     */
    private int nextRow(int row, int col) {
        return col + 1 < sudoku.length ? row : row + 1;
    }
 
    /**
     * returns the next col
     * @param row current row
     * @param col current col
     * @return next col
     */
    private int nextCol(int row, int col) {
        return col + 1 < sudoku.length ? col + 1 : 0;
    }
 
    /**
     * returns all possibilities for the current field
     * @param row current row
     * @param col current col
     * @return all possibilities in a int array
     */
    private int[] getPossibilities(int row, int col) {
        CoatSet cs = new CoatSet(10);
        for (int i = 0; i < sudoku.length; i++) {
            cs.coat(sudoku[row][i]);
            cs.coat(sudoku[i][col]);
        }
        int rowStart = row - row % 3, colStart = col - col % 3;
        for (int r = rowStart; r < rowStart + 3; r++) {
            for (int c = colStart; c < colStart + 3; c++)
                cs.coat(sudoku[r][c]);
        }
        return cs.getUncoated();
    }
 
    /**
     * returns a String representing the sudoku
     * @return String representation of the sudoku
     */
    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder();
        final String lineSep = System.getProperty("line.separator");
        final char space = ' ';
        for (int[] a : sudoku) {
            for (int i = 0; i < a.length; i++) {
                if (i > 0) sb.append(space);
                sb.append(a[i]);
            }
            sb.append(lineSep);
        }
        return sb.toString();
    }
 
    /**
     * private class to coat numbers
     * @author nrg
     */
    private class CoatSet {
 
        private boolean[] set;
        private int uncoated;
 
        /**
         * Constructs a coatset of the given size 
         * @param size size of the coatset
         */
        private CoatSet(int size) {
            this.uncoated = size;
            this.set = new boolean[size];
            for (int i = 0; i < set.length; i++)
                set[i] = true;
        }
 
        /**
         * coats a number
         * @param n the number
         * @throws ArrayIndexOutOfBoundsException if n < 0 or n >= size
         */
        private void coat(int n) {
            if (set[n]) uncoated--;
            set[n] = false;
        }
 
        /**
         * returns all uncoated numbers
         * @return a int-array contains all uncoated numbers
         */
        private int[] getUncoated() {
            int[] array = new int[uncoated];
            for (int i = 1, j = 0; i < set.length; i++)
                if (set[i]) array[j++] = i;
            return array;
        }
    }
 
    /**
     * parses a string-array to a int-array
     * @param a the string array
     * @return the int array
     * @throws InvalidSudokuException if any field != point or field != [1-9]
     */
    private static int[] parseLine(String[] a) {
        int[] array = new int[a.length];
        for (int i = 0; i < a.length; i++) {        
            if (!a[i].matches("[1-9]|\\."))
                throw new InvalidSudokuException("at field " + a[i]);
            array[i] = a[i].equals(".") ? 0 : Integer.parseInt(a[i]);
        }
        return array;
    }
}

Java Code:

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import java.io.IOException;
 
public class SudokuSolverTest {
 
    public static void main(String[] args) {    
        SudokuSolver ss = new SudokuSolver(new int[][] {
                {2, 0, 7, 0, 8, 6, 0, 0, 0},
                {0, 0, 5, 0, 7, 1, 0, 0, 8},
                {0, 9, 8, 0, 4, 0, 1, 7, 6},
                {0, 0, 4, 0, 0, 9, 0, 0, 7},
                {0, 8, 0, 7, 0, 5, 0, 3, 0},
                {0, 0, 0, 4, 0, 0, 9, 2, 5},
                {8, 0, 3, 0, 0, 0, 0, 5, 2},
                {7, 0, 0, 0, 2, 0, 3, 0, 0},
                {0, 0, 0, 6, 5, 0, 0, 0, 1},
        });
        
        System.out.println("solved in " + ss.solve()/1000000. + " milliseconds");
        System.out.println(ss);
    }
}

Java Code:

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public class InvalidSudokuException extends RuntimeException {
 
    private static final long serialVersionUID = 1L;
 
    public InvalidSudokuException(String msg) {
        super(msg);
    }
}

Java Code:

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public class UnsolveableSudokuException extends RuntimeException {
 
    private static final long serialVersionUID = 1L;
 
    public UnsolveableSudokuException(String msg) {
        super(msg);
    }
}

solved in 2.372598 milliseconds
2 1 7 9 8 6 5 4 3
6 4 5 3 7 1 2 9 8
3 9 8 5 4 2 1 7 6
5 3 4 2 6 9 8 1 7
9 8 2 7 1 5 6 3 4
1 7 6 4 3 8 9 2 5
8 6 3 1 9 7 4 5 2
7 5 1 8 2 4 3 6 9
4 2 9 6 5 3 7 8 1