八皇后问题 --- 递归解法 --- java代码

八皇后问题是一个以国际象棋为背景的问题：如何能够在 8×8 的国际象棋棋盘上放置八个皇后，使得任何一个皇后都无法直接吃掉其他的皇后？为了达到此目的，任两个皇后都不能处于同一条横行、纵行或斜线上。八皇后问题可以推广为更一般的n皇后摆放问题：这时棋盘的大小变为n×n，而皇后个数也变成n。当且仅当 n = 1 或 n ≥ 4 时问题有解[1]。
以上内容摘自维基百科：http://zh.wikipedia.org/wiki/%E5%85%AB%E7%9A%87%E5%90%8E%E9%97%AE%E9%A2%98

代码如下：

public class Demo {

    public static void main(String[] args) {
        nextRowPlace(START_ROW);
    }

    private static final int ROW = 8, COL = 8, START_ROW = 0, START_COL = 0;
    private static boolean[][] board = new boolean[8][8];

    private static void nextRowPlace(final int row) {
        if(row == ROW){
            print();
            return;
        }
        for(int j=START_COL; j!=COL; ++j)
            if(checkPosValid(row, j)){
                board[row][j] = true;
                nextRowPlace(row+1);
                board[row][j] = false;
            }
        return;
    }

    private static boolean checkPosValid(final int row, final int col) {
        for(int i=START_ROW; i!=ROW; ++i)
            if(board[i][col])
                return false;
        for(int i=row, j=col; i!=START_ROW-1 && j!=START_COL-1; --i, --j)
            if(board[i][j])
                return false;
        for(int i=row, j=col; i!=START_ROW-1 && j!= COL; --i, ++j)
            if(board[i][j])
                return false;
        return true;
    }

    private static int count = 0;
    private static void print() {
        System.out.println("--- --- --- --- --- " + ++count +" --- ---");
        for(int i=START_ROW; i!=ROW; ++i){
            for(int j=START_COL; j!=COL; ++j)
                System.out.print(board[i][j] ? "O " : "X ");
            System.out.println();
        }
        System.out.println();
        return;
    }

}

运行结果如下：

--- --- --- --- --- 1 --- ---
O X X X X X X X
X X X X O X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X O X X X X 

--- --- --- --- --- 2 --- ---
O X X X X X X X
X X X X X O X X
X X X X X X X O
X X O X X X X X
X X X X X X O X
X X X O X X X X
X O X X X X X X
X X X X O X X X 

--- --- --- --- --- 3 --- ---
O X X X X X X X
X X X X X X O X
X X X O X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X X O X X X
X X O X X X X X 

--- --- --- --- --- 4 --- ---
O X X X X X X X
X X X X X X O X
X X X X O X X X
X X X X X X X O
X O X X X X X X
X X X O X X X X
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 5 --- ---
X O X X X X X X
X X X O X X X X
X X X X X O X X
X X X X X X X O
X X O X X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X 

--- --- --- --- --- 6 --- ---
X O X X X X X X
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X 

--- --- --- --- --- 7 --- ---
X O X X X X X X
X X X X O X X X
X X X X X X O X
X X X O X X X X
O X X X X X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 8 --- ---
X O X X X X X X
X X X X X O X X
O X X X X X X X
X X X X X X O X
X X X O X X X X
X X X X X X X O
X X O X X X X X
X X X X O X X X 

--- --- --- --- --- 9 --- ---
X O X X X X X X
X X X X X O X X
X X X X X X X O
X X O X X X X X
O X X X X X X X
X X X O X X X X
X X X X X X O X
X X X X O X X X 

--- --- --- --- --- 10 --- ---
X O X X X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X
X X X X X X X O
X X X X O X X X
O X X X X X X X
X X X O X X X X 

--- --- --- --- --- 11 --- ---
X O X X X X X X
X X X X X X O X
X X X X O X X X
X X X X X X X O
O X X X X X X X
X X X O X X X X
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 12 --- ---
X O X X X X X X
X X X X X X X O
X X X X X O X X
O X X X X X X X
X X O X X X X X
X X X X O X X X
X X X X X X O X
X X X O X X X X 

--- --- --- --- --- 13 --- ---
X X O X X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X
X X X X X X X O
X O X X X X X X
X X X O X X X X
X X X X X O X X 

--- --- --- --- --- 14 --- ---
X X O X X X X X
X X X X O X X X
X O X X X X X X
X X X X X X X O
O X X X X X X X
X X X X X X O X
X X X O X X X X
X X X X X O X X 

--- --- --- --- --- 15 --- ---
X X O X X X X X
X X X X O X X X
X O X X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X
X X X X X X O X
O X X X X X X X 

--- --- --- --- --- 16 --- ---
X X O X X X X X
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X X O X X 

--- --- --- --- --- 17 --- ---
X X O X X X X X
X X X X O X X X
X X X X X X X O
X X X O X X X X
O X X X X X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X 

--- --- --- --- --- 18 --- ---
X X O X X X X X
X X X X X O X X
X O X X X X X X
X X X X O X X X
X X X X X X X O
O X X X X X X X
X X X X X X O X
X X X O X X X X 

--- --- --- --- --- 19 --- ---
X X O X X X X X
X X X X X O X X
X O X X X X X X
X X X X X X O X
O X X X X X X X
X X X O X X X X
X X X X X X X O
X X X X O X X X 

--- --- --- --- --- 20 --- ---
X X O X X X X X
X X X X X O X X
X O X X X X X X
X X X X X X O X
X X X X O X X X
O X X X X X X X
X X X X X X X O
X X X O X X X X 

--- --- --- --- --- 21 --- ---
X X O X X X X X
X X X X X O X X
X X X O X X X X
O X X X X X X X
X X X X X X X O
X X X X O X X X
X X X X X X O X
X O X X X X X X 

--- --- --- --- --- 22 --- ---
X X O X X X X X
X X X X X O X X
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X O X X X
X X X X X X O X
O X X X X X X X 

--- --- --- --- --- 23 --- ---
X X O X X X X X
X X X X X O X X
X X X X X X X O
O X X X X X X X
X X X O X X X X
X X X X X X O X
X X X X O X X X
X O X X X X X X 

--- --- --- --- --- 24 --- ---
X X O X X X X X
X X X X X O X X
X X X X X X X O
O X X X X X X X
X X X X O X X X
X X X X X X O X
X O X X X X X X
X X X O X X X X 

--- --- --- --- --- 25 --- ---
X X O X X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X O X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X 

--- --- --- --- --- 26 --- ---
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X X X X X O
X X X X O X X X
O X X X X X X X
X X X O X X X X
X X X X X O X X 

--- --- --- --- --- 27 --- ---
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X
O X X X X X X X
X X X X O X X X 

--- --- --- --- --- 28 --- ---
X X O X X X X X
X X X X X X X O
X X X O X X X X
X X X X X X O X
O X X X X X X X
X X X X X O X X
X O X X X X X X
X X X X O X X X 

--- --- --- --- --- 29 --- ---
X X X O X X X X
O X X X X X X X
X X X X O X X X
X X X X X X X O
X O X X X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X 

--- --- --- --- --- 30 --- ---
X X X O X X X X
O X X X X X X X
X X X X O X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X
X X X X X X O X
X O X X X X X X 

--- --- --- --- --- 31 --- ---
X X X O X X X X
X O X X X X X X
X X X X O X X X
X X X X X X X O
X X X X X O X X
O X X X X X X X
X X O X X X X X
X X X X X X O X 

--- --- --- --- --- 32 --- ---
X X X O X X X X
X O X X X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X
X X X X X X X O
O X X X X X X X
X X X X O X X X 

--- --- --- --- --- 33 --- ---
X X X O X X X X
X O X X X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X
X X X X X X X O
X X X X O X X X
O X X X X X X X 

--- --- --- --- --- 34 --- ---
X X X O X X X X
X O X X X X X X
X X X X X X O X
X X X X O X X X
O X X X X X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 35 --- ---
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X X O X X 

--- --- --- --- --- 36 --- ---
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X X O X X
O X X X X X X X
X X O X X X X X
X X X X O X X X
X X X X X X O X 

--- --- --- --- --- 37 --- ---
X X X O X X X X
X X X X X O X X
O X X X X X X X
X X X X O X X X
X O X X X X X X
X X X X X X X O
X X O X X X X X
X X X X X X O X 

--- --- --- --- --- 38 --- ---
X X X O X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X O X X X 

--- --- --- --- --- 39 --- ---
X X X O X X X X
X X X X X O X X
X X X X X X X O
X X O X X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X
X O X X X X X X 

--- --- --- --- --- 40 --- ---
X X X O X X X X
X X X X X X O X
O X X X X X X X
X X X X X X X O
X X X X O X X X
X O X X X X X X
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 41 --- ---
X X X O X X X X
X X X X X X O X
X X O X X X X X
X X X X X X X O
X O X X X X X X
X X X X O X X X
O X X X X X X X
X X X X X O X X 

--- --- --- --- --- 42 --- ---
X X X O X X X X
X X X X X X O X
X X X X O X X X
X O X X X X X X
X X X X X O X X
O X X X X X X X
X X O X X X X X
X X X X X X X O 

--- --- --- --- --- 43 --- ---
X X X O X X X X
X X X X X X O X
X X X X O X X X
X X O X X X X X
O X X X X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X 

--- --- --- --- --- 44 --- ---
X X X O X X X X
X X X X X X X O
O X X X X X X X
X X O X X X X X
X X X X X O X X
X O X X X X X X
X X X X X X O X
X X X X O X X X 

--- --- --- --- --- 45 --- ---
X X X O X X X X
X X X X X X X O
O X X X X X X X
X X X X O X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 46 --- ---
X X X O X X X X
X X X X X X X O
X X X X O X X X
X X O X X X X X
O X X X X X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X 

--- --- --- --- --- 47 --- ---
X X X X O X X X
O X X X X X X X
X X X O X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X X X X O X
X X O X X X X X 

--- --- --- --- --- 48 --- ---
X X X X O X X X
O X X X X X X X
X X X X X X X O
X X X O X X X X
X O X X X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X 

--- --- --- --- --- 49 --- ---
X X X X O X X X
O X X X X X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X O X X X X 

--- --- --- --- --- 50 --- ---
X X X X O X X X
X O X X X X X X
X X X O X X X X
X X X X X O X X
X X X X X X X O
X X O X X X X X
O X X X X X X X
X X X X X X O X 

--- --- --- --- --- 51 --- ---
X X X X O X X X
X O X X X X X X
X X X O X X X X
X X X X X X O X
X X O X X X X X
X X X X X X X O
X X X X X O X X
O X X X X X X X 

--- --- --- --- --- 52 --- ---
X X X X O X X X
X O X X X X X X
X X X X X O X X
O X X X X X X X
X X X X X X O X
X X X O X X X X
X X X X X X X O
X X O X X X X X 

--- --- --- --- --- 53 --- ---
X X X X O X X X
X O X X X X X X
X X X X X X X O
O X X X X X X X
X X X O X X X X
X X X X X X O X
X X O X X X X X
X X X X X O X X 

--- --- --- --- --- 54 --- ---
X X X X O X X X
X X O X X X X X
O X X X X X X X
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X O X X X X
X X X X X X O X 

--- --- --- --- --- 55 --- ---
X X X X O X X X
X X O X X X X X
O X X X X X X X
X X X X X X O X
X O X X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X 

--- --- --- --- --- 56 --- ---
X X X X O X X X
X X O X X X X X
X X X X X X X O
X X X O X X X X
X X X X X X O X
O X X X X X X X
X X X X X O X X
X O X X X X X X 

--- --- --- --- --- 57 --- ---
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X
X O X X X X X X 

--- --- --- --- --- 58 --- ---
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 59 --- ---
X X X X O X X X
X X X X X X O X
X O X X X X X X
X X X O X X X X
X X X X X X X O
O X X X X X X X
X X O X X X X X
X X X X X O X X 

--- --- --- --- --- 60 --- ---
X X X X O X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X
X X O X X X X X
O X X X X X X X
X X X O X X X X
X X X X X X X O 

--- --- --- --- --- 61 --- ---
X X X X O X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X
X X O X X X X X
O X X X X X X X
X X X X X X X O
X X X O X X X X 

--- --- --- --- --- 62 --- ---
X X X X O X X X
X X X X X X O X
X X X O X X X X
O X X X X X X X
X X O X X X X X
X X X X X X X O
X X X X X O X X
X O X X X X X X 

--- --- --- --- --- 63 --- ---
X X X X O X X X
X X X X X X X O
X X X O X X X X
O X X X X X X X
X X O X X X X X
X X X X X O X X
X O X X X X X X
X X X X X X O X 

--- --- --- --- --- 64 --- ---
X X X X O X X X
X X X X X X X O
X X X O X X X X
O X X X X X X X
X X X X X X O X
X O X X X X X X
X X X X X O X X
X X O X X X X X 

--- --- --- --- --- 65 --- ---
X X X X X O X X
O X X X X X X X
X X X X O X X X
X O X X X X X X
X X X X X X X O
X X O X X X X X
X X X X X X O X
X X X O X X X X 

--- --- --- --- --- 66 --- ---
X X X X X O X X
X O X X X X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X O X X X
X X X X X X X O
X X X O X X X X 

--- --- --- --- --- 67 --- ---
X X X X X O X X
X O X X X X X X
X X X X X X O X
O X X X X X X X
X X X O X X X X
X X X X X X X O
X X X X O X X X
X X O X X X X X 

--- --- --- --- --- 68 --- ---
X X X X X O X X
X X O X X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X
X X X X X X X O
X O X X X X X X
X X X O X X X X 

--- --- --- --- --- 69 --- ---
X X X X X O X X
X X O X X X X X
O X X X X X X X
X X X X X X X O
X X X O X X X X
X O X X X X X X
X X X X X X O X
X X X X O X X X 

--- --- --- --- --- 70 --- ---
X X X X X O X X
X X O X X X X X
O X X X X X X X
X X X X X X X O
X X X X O X X X
X O X X X X X X
X X X O X X X X
X X X X X X O X 

--- --- --- --- --- 71 --- ---
X X X X X O X X
X X O X X X X X
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X X O X X X X
X O X X X X X X
X X X X X X X O 

--- --- --- --- --- 72 --- ---
X X X X X O X X
X X O X X X X X
X X X X O X X X
X X X X X X X O
O X X X X X X X
X X X O X X X X
X O X X X X X X
X X X X X X O X 

--- --- --- --- --- 73 --- ---
X X X X X O X X
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X O X X X X
X X X X X X X O
O X X X X X X X
X X X X O X X X 

--- --- --- --- --- 74 --- ---
X X X X X O X X
X X O X X X X X
X X X X X X O X
X O X X X X X X
X X X X X X X O
X X X X O X X X
O X X X X X X X
X X X O X X X X 

--- --- --- --- --- 75 --- ---
X X X X X O X X
X X O X X X X X
X X X X X X O X
X X X O X X X X
O X X X X X X X
X X X X X X X O
X O X X X X X X
X X X X O X X X 

--- --- --- --- --- 76 --- ---
X X X X X O X X
X X X O X X X X
O X X X X X X X
X X X X O X X X
X X X X X X X O
X O X X X X X X
X X X X X X O X
X X O X X X X X 

--- --- --- --- --- 77 --- ---
X X X X X O X X
X X X O X X X X
X O X X X X X X
X X X X X X X O
X X X X O X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X 

--- --- --- --- --- 78 --- ---
X X X X X O X X
X X X O X X X X
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X O X X X
X O X X X X X X
X X X X X X X O 

--- --- --- --- --- 79 --- ---
X X X X X O X X
X X X O X X X X
X X X X X X O X
O X X X X X X X
X X X X X X X O
X O X X X X X X
X X X X O X X X
X X O X X X X X 

--- --- --- --- --- 80 --- ---
X X X X X O X X
X X X X X X X O
X O X X X X X X
X X X O X X X X
O X X X X X X X
X X X X X X O X
X X X X O X X X
X X O X X X X X 

--- --- --- --- --- 81 --- ---
X X X X X X O X
O X X X X X X X
X X O X X X X X
X X X X X X X O
X X X X X O X X
X X X O X X X X
X O X X X X X X
X X X X O X X X 

--- --- --- --- --- 82 --- ---
X X X X X X O X
X O X X X X X X
X X X O X X X X
O X X X X X X X
X X X X X X X O
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2014-04-12

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