解法1， 按行回溯：

import java.io.*;
class Main{
    static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
    static char[][] cs;
    static boolean[] dg, udg, col;
    public static void main(String[] args) throws Exception{
        int n = Integer.valueOf(read.readLine());
        cs = new char[n][n];
        dg = new boolean[n * 2];  udg = new boolean[n * 2]; col = new boolean[n];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                cs[i][j] = '.';
            }
        }
        bc(0, n);
    }

    public static void bc(int i, int n){
        if(i == n){
            for(int k = 0; k < n; k++) System.out.println(cs[k]);
            System.out.println();
            return;
        }
        for(int j = 0; j < n; j++){
            if(!col[j] && !dg[i + j] && !udg[j - i + n]){
                cs[i][j] = 'Q';
                col[j] = dg[i + j] = udg[j - i + n] = true;
                bc(i + 1, n);
                col[j] = dg[i + j] = udg[j - i + n] = false;
                cs[i][j] = '.';
            }
        }
    }
}

解法二， 枚举回溯：

import java.io.*;
class Main{
    static BufferedReader read = new BufferedReader(new InputStreamReader(System.in));
    static char[][] cs;
    static boolean[] dg, udg, col, row;
    public static void main(String[] args) throws Exception{
        int n = Integer.valueOf(read.readLine());
        cs = new char[n][n];
        dg = new boolean[n * 2];  udg = new boolean[n * 2]; 
        col = new boolean[n]; row = new boolean[n];
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                cs[i][j] = '.';
            }
        }
        bc(0, 0, 0, n);
    }

    public static void bc(int i, int j, int queueNum, int n){
        if(j == n)   {j = 0; i++;}
        if(i == n){
            if(queueNum == n){
                for(int k = 0; k < n; k++)  System.out.println(cs[k]);
                System.out.println();
            }
            return;
        }
        //不放皇后
        bc(i, j + 1, queueNum, n);
        //放皇后
        if(!row[i] && !col[j] && !udg[j - i + n] && !dg[i + j]){
            cs[i][j] = 'Q';
            row[i] = col[j] = dg[i + j] = udg[j - i + n] = true;
            bc(i, j + 1, queueNum + 1, n);
            row[i] = col[j] = dg[i + j] = udg[j - i + n] = false;
            cs[i][j] = '.';
        }
    }
}