通过排列行枚举实现n皇后问题

import java.io.*;

public class Main{
    static int N=20;
    static char[][] ordered;
    static boolean[] col,dg,udg;
    static int nn;
    public static void main(String[] args)throws IOException{
        BufferedReader cin=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(cin.readLine());
        nn=n;
        ordered=new char[N][N];
        col=new boolean[N];dg=new boolean[N];
        udg=new boolean[N];
        //初始化ordered
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                ordered[i][j]='.';
            }
        }
        dfs(0);
    }

    public static void dfs(int cur){
        if(cur==nn){
            for(int i=0;i<nn;i++){
                for(int j=0;j<nn;j++){
                    System.out.print(ordered[i][j]);   
                }
                System.out.println();
            }
            System.out.println();
            return;
        }
        //对于每一列
        for(int i=0;i<nn;i++){
            if(!col[i]&&!dg[cur+i]&&!udg[cur-i+nn]){
                col[i]=dg[cur+i]=udg[cur-i+nn]=true;
                ordered[cur][i]='Q';
                dfs(cur+1);
                col[i]=dg[cur+i]=udg[cur-i+nn]=false;
                ordered[cur][i]='.';
            }
        }
    }

}

对每一个格子进行搜索

import java.io.*;

public class Main{

    static int N=20;

    static char[][] ordered;
    static boolean[] row,col,dg,udg;
    static int nn;
    public static void main(String[] args)throws IOException{
        BufferedReader cin=new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(cin.readLine());
        ordered=new char[N][N];
        row=new boolean[N];col=new boolean[N];dg=new boolean[N];udg=new boolean[N];
        nn=n;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                ordered[i][j]='.';
            }
        }
        dfs(0,0,0);
    }

    public static void dfs(int i,int j,int cnt){
        if(j==nn){
            j=0;i++;//下一行
        }
        if(i==nn){
            if(cnt==nn){
             for(int ii=0;ii<nn;ii++){
                for(int jj=0;jj<nn;jj++){
                    System.out.print(ordered[ii][jj]);
                }
                System.out.println();
            }
            System.out.println();   
            }
            return;
        }

        //两个分支

        //不妨皇后，直接dfs
        dfs(i,j+1,cnt);

        //放，是否能放
        if(!row[i]&&!col[j]&&!dg[i+j]&&!udg[i-j+nn]){
            //放完之后，修改状态
            ordered[i][j]='Q';
            row[i]=col[j]=dg[i+j]=udg[i-j+nn]=true;
            dfs(i,j+1,cnt+1);
            ordered[i][j]='.';
            row[i]=col[j]=dg[i+j]=udg[i-j+nn]=false;
        }

    }
}