java - 八皇后算法

Question

我之前问过一个关于使用 Java 解决八皇后问题的问题。 我得到了一个回溯算法来解决这个问题。

我尝试使用这个算法，但我不知道我的代码有什么问题。它最多只能放置 7 个皇后。

这是皇后类:

    public class Queen {
    //Number of rows or columns
    public static final int BOARD_SIZE = 8;

    boolean[][] board;
    //Indicate an empty square
    public static final boolean EMPTY = false;
    //Indicate a square which containing a queen
    public static final boolean QUEEN = true;
    //Number of moves
    public static final int MOVES = 4;
    //Horizontal moves
    int[] horizontal;
    //Vertical moves
    int[] vertical;

    public int queens = 0;

    public Queen() {
        //Constructor creates an empty board
        board = new boolean[BOARD_SIZE][BOARD_SIZE];
        for (int row = 0; row < board.length; row++) {
            for (int col = 0; col < board[row].length; col++) {
                board[row][col] = EMPTY;
            }
        }

        horizontal = new int[MOVES];
        vertical = new int[MOVES];
        // up right
        horizontal[0] = -1;
        vertical[0] = 1; 
        // down left
        horizontal[1] = 1;
        vertical[1] = -1;
        // up left
        horizontal[2] = -1;
        vertical[2] = -1;
        // down right
        horizontal[3] = 1;
        vertical[3] = 1;
    }

    public boolean placeQueens (int column) {
        if (column > BOARD_SIZE) {
            return true;
        }
        else {
            boolean queenPlaced = false;
            int row = 1;

            while (!queenPlaced && row < BOARD_SIZE) {
                if (isUnderAttack(row, column)) {
                    ++row;
                }// end if
                else{
                    setQueen(row, column);
                    queenPlaced = placeQueens(column + 1);
                    if (!queenPlaced) {
                        removeQueen(row,column);
                        ++row;
                    }// end if
                }// end else
            }// end while
            return queenPlaced;
        }// end else
    }

    private void removeQueen(int row, int column) {
        board[row][column] = EMPTY;
        System.out.printf("queen REMOVED from [%d][%d]\n", row, column);
    --queens;
    }

    private void setQueen(int row, int column) {
        board[row][column] = QUEEN;
        System.out.printf("queen PLACED in [%d][%d]\n", row, column);
        ++queens;
    }

    public boolean isUnderAttack(int row, int col) {
        boolean condition = false;
        // check row
        for (int column = 0; column < BOARD_SIZE; column++) {
            if ((board[row][column] == true)) {
                condition = true;
            }
        }

        // check column
        for (int row_ = 0; row_ < board.length; row_++) {
            if (board[row_][col] == true) {
                        condition = true;
            }
        }

        // check diagonal
        for (int row_ = row, col_ = col; row_ >= 0 && col_ < 8; row_ += horizontal[0], col_ += vertical[0]) {
            if (board[row_][col_] == true) {
                condition = true;
            }
        }
        for (int row_ = row, col_ = col; row_ < 8 && col_ >= 0; row_ += horizontal[1], col_ += vertical[1]) {
            if (board[row_][col_] == true) {
                condition = true;
            }
        }
        for (int row_ = row, col_ = col; row_ >= 0 && col_ >= 0; row_ += horizontal[2], col_ += vertical[2]) {
            if (board[row_][col_] == true) {
                condition = true;
            }
        }
        for (int row_ = row, col_ = col; row_ < 8 && col_ < 8; row_ += horizontal[3], col_ += vertical[3]) {
            if (board[row_][col_] == true) {
                condition = true;
            }
        }

        return condition;
    }

    public void displayBoard () {
        int counter = 0;
        for (int row = 0; row < board.length; row++) {
            for (int col = 0; col < board[row].length; col++) {
                if (board[row][col] == true) {
                    System.out.printf("|%s|", "x");
                    counter++;
                }
                else {              
                    System.out.printf("|%s|", "o");
                }
            }
            System.out.println();
        }

        System.out.printf("%d queens has been placed\n", counter);
    }
}

Answer 1

在 Java 中数组是 0-indexed ，这意味着第一项在索引 0 处。您似乎没有完全掌握这个关键事实，这导致您编写的代码中有许多 off-by-one errors。 .

这里有一个问题:

int row = 1;

应该是:

int row = 0;

---

第二个问题是:

if (column > BOARD_SIZE) {
    return true;
}

应该是这样的:

if (column >= BOARD_SIZE) {
    return true;
}

---

您还没有发布其余代码，但我敢打赌，当您调用 placeQueens 方法时，您的代码中存在第三个错误。如果我知道你是什么样的人，那么你可能会这样做:

queen.placeQueens(1);

但应该是这样的:

queen.placeQueens(0);

---

通过所有这些更改，它可以按预期工作。最终结果是:

|x||o||o||o||o||o||o||o|
|o||o||o||o||o||o||x||o|
|o||o||o||o||x||o||o||o|
|o||o||o||o||o||o||o||x|
|o||x||o||o||o||o||o||o|
|o||o||o||x||o||o||o||o|
|o||o||o||o||o||x||o||o|
|o||o||x||o||o||o||o||o|
8 queens has been placed

在线查看它:ideone