2、八皇后问题——回溯法

/**
 *
 */
package unit1;

/**
 * @author
 * @version 创建时间：2015-10-30 下午02:55:24 类说明
 */
public class EightQueensNotRecursive {
    private static final boolean AVAILABLE = true;
    private int squares = 16, norm = squares - 1;
    private int positionInRow[] = new int[squares];
    private int p = -1;
    private boolean[] rows = new boolean[squares];
    private boolean[] column = new boolean[squares];
    private boolean[] leftDiagonal = new boolean[2 * squares - 1];
    private boolean[] rightDiagonal = new boolean[2 * squares - 1];
    private static int howMany = 0;

    public EightQueensNotRecursive() {
        // To complete the initialization work for the
        // column,leftDiagonal,rigthDiagonal.
        for (int i = 0; i < squares; i++) {
            rows[i] = AVAILABLE;
            column[i] = AVAILABLE;
            positionInRow[i] = -1;
        }
        for (int i = 0; i < 2 * squares - 1; i++) {
            leftDiagonal[i] = AVAILABLE;
            rightDiagonal[i] = AVAILABLE;
        }

    }

    public void printResults(int[] columns) {
        int row, col;
        System.out.println("八皇后问题的第 " + howMany + " 种解法");
        System.out.print("八皇后问题的结果为：");
        for (int e : columns) {
            System.out.print(e);
        }
        System.out.println("\n具体的图示如下图所示：");
        for (row = 0; row < squares; row++) {
            for (col = 0; col < squares; col++) {
                if (col == positionInRow[row]) {
                    System.out.print("@");
                } else {
                    System.out.print("*");
                }
            }
            System.out.println();
        }
        System.out.println();
    }

    public void putQueen() {
        int row = 0, col;
        while (true) {
            for (col = p + 1; col < squares; col++) {
                if (rows[row] == AVAILABLE && column[col] == AVAILABLE
                        && leftDiagonal[row + col] == AVAILABLE
                        && rightDiagonal[row - col + norm] == AVAILABLE) {
                    break;
                }
            }
            // 在当前的行里面找到了可以放置皇后的位置
            if (col < squares) {
                rows[row] = !AVAILABLE;
                column[col] = !AVAILABLE;
                leftDiagonal[row + col] = !AVAILABLE;
                rightDiagonal[row - col + norm] = !AVAILABLE;
                positionInRow[row] = col;
                p = col;
            } else// 如果当前行没办反放置皇后了，那么回溯
            {
                if (row > 0)// 到前一行
                {
                    row--;
                    p = positionInRow[row];
                    rows[row] = AVAILABLE;
                    column[p] = AVAILABLE;
                    leftDiagonal[row + p] = AVAILABLE;
                    rightDiagonal[row - p + norm] = AVAILABLE;
                    positionInRow[row] = -1;
                    continue;
                } else {
                    break;
                }
            }
            if (row == squares - 1) {
                howMany += 1;
                printResults(positionInRow);
                p = positionInRow[row];
                rows[row] = AVAILABLE;
                column[p] = AVAILABLE;
                leftDiagonal[row + p] = AVAILABLE;
                rightDiagonal[row - p + norm] = AVAILABLE;
                positionInRow[row] = -1;
                continue;
            } else {
                row++;
                p = -1;
                continue;
            }
        }
    }

    public static void main(String args[]) {
        EightQueensNotRecursive eightQueens = new EightQueensNotRecursive();
        eightQueens.putQueen();
        System.out.println("皇后问题一共有" + howMany + "种解法");
    }

}

/**
 *
 */
package unit1;

/**
 * @author
 * @version 创建时间：2015-10-30 下午02:41:57 类说明
 */
public class EightQueensRecursive {
    private static final boolean AVAILABLE = true;
    private int squares = 8, norm = squares - 1;
    private int positionInRow[] = new int[squares];
    private boolean[] column = new boolean[squares];
    private boolean[] leftDiagonal = new boolean[2 * squares - 1];
    private boolean[] rightDiagonal = new boolean[2 * squares - 1];
    private static int howMany = 0;

    public EightQueensRecursive() {
        // To complete the initialization work for the
        // column,leftDiagonal,rigthDiagonal.
        for (int i = 0; i < squares; i++) {
            column[i] = AVAILABLE;
            positionInRow[i] = -1;
        }
        for (int i = 0; i < 2 * squares - 1; i++) {
            leftDiagonal[i] = AVAILABLE;
            rightDiagonal[i] = AVAILABLE;
        }
    }

    public void printResults(int[] columns) {
        int row, col;
        System.out.println("八皇后问题的第 " + howMany + " 种解法");
        System.out.print("八皇后问题的结果为：");
        for (int e : columns) {
            System.out.print(e);
        }
        System.out.println("\n具体的图示如下图所示：");
        for (row = 0; row < squares; row++) {
            for (col = 0; col < squares; col++) {
                if (col == positionInRow[row]) {
                    System.out.print("@");
                } else {
                    System.out.print("*");
                }
            }
            System.out.println();
        }
        System.out.println();
    }

    public void putQueen(int row) {
        // 如果前面已经得到了一个可行解
        for (int i = 0; i < squares; i++) {
            if (row > squares - 1)
                break;
            if (column[i] == AVAILABLE && leftDiagonal[row + i] == AVAILABLE
                    && rightDiagonal[row - i + norm] == AVAILABLE) {
                positionInRow[row] = i;
                column[i] = !AVAILABLE;
                leftDiagonal[row + i] = !AVAILABLE;
                rightDiagonal[row - i + norm] = !AVAILABLE;
                if (row < squares - 1) {
                    putQueen(row + 1);
                } else {
                    howMany += 1;
                    printResults(positionInRow);
                }
                column[i] = AVAILABLE;
                leftDiagonal[row + i] = AVAILABLE;
                rightDiagonal[row - i + norm] = AVAILABLE;
            }
        }
    }

    public static void main(String args[]) {
        EightQueensRecursive eightQueens = new EightQueensRecursive();
        eightQueens.putQueen(0);
        System.out.println("皇后问题一共找到了 " + howMany + "组解。");
    }
}