• 原题链接：51. N 皇后

1- 思路

使用回溯的方式实现，回溯三部曲

• 数据结构：定义三维数组，收集结果
• 1- 回溯终止条件：如果遍历到 row == n-1 此时就是结果收集的时刻
• 2- 执行 for 循环遍历，执行递归和回溯

2- 实现

⭐51. N 皇后——题解思路

class Solution {
    List<List<String>> res = new ArrayList<>();
    public List<List<String>> solveNQueens(int n) {
        char[][] cheesBoard = new char[n][n];
        for(char[] c:cheesBoard){
            Arrays.fill(c,'.');
        }
        backTracing(n,0,cheesBoard);
        return res;
    }

    private void backTracing(int n,int row,char[][] cheesBoard){
        // 1.终止条件收集结果
        if(row==n){
            res.add(Array2List(cheesBoard));
            return ;
        }

        // 2. 遍历
        for(int i = 0; i < n ; i++){
            if(isValid(row,i,n,cheesBoard)){
                cheesBoard[row][i] = 'Q';
                backTracing(n,row+1,cheesBoard);
                cheesBoard[row][i] = '.';
            }
        }
    }

    private List<String> Array2List(char[][] cheesBoard){
        List<String> list = new ArrayList<>();
        for(char[] c:cheesBoard){
            list.add(String.copyValueOf(c));
        }
        return list;
    }


    private boolean isValid(int row,int col,int n,char[][] cheesBoard){

        // 列
        for (int i = 0; i < row; i++) {
            if (cheesBoard[i][col] == 'Q') {
                return false;
            }
        }


        /// 45
        for(int i = row-1,j = col-1;i>=0 && j>=0;i--,j--){
            if(cheesBoard[i][j] == 'Q'){
                return false;
            }
        }

        // 135
        for(int i = row-1,j = col+1;i>=0 && j<n;i--, j++){
            if(cheesBoard[i][j] == 'Q'){
                return false;
            }
        }
        return true;
    }
}

3- ACM 实现

package Daily_LC.Month8_Week2.Day124;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Scanner;

/**
 * NQueens
 *
 * @author alcohol
 * @Description
 * @since 2024-08-09 10:28
 */
public class NQueens {

    static List<List<String>> res = new ArrayList<>();
    public static List<List<String>> nQueens(int n){
        char[][] cheesBoard = new char[n][n];
        for(char[] c:cheesBoard){
            Arrays.fill(c,'.');
        }
        backTracing(n,0,cheesBoard);
        return res;
    }

    public static void backTracing(int n,int row,char[][] cheesBoard){
        // 1. 终止条件
        if(row==n){
            res.add(Array2List(cheesBoard));
            return;
        }
        // 2. 遍历
        for(int i = 0 ; i < n;i++){
            if(isValid(row,i,n,cheesBoard)){
                cheesBoard[row][i] = 'Q';
                backTracing(n,row+1,cheesBoard);
                cheesBoard[row][i] = '.';
            }
        }
    }


    private static List<String> Array2List(char[][] cheesBoard){
        List<String> list = new ArrayList<>();
        for(char[] c: cheesBoard){
            list.add(String.copyValueOf(c));
        }
        return list;
    }


    private static boolean isValid(int row, int col,int n, char[][] cheesBoard){
        // 列
        for(int i = 0 ; i < row;i++){
            if(cheesBoard[i][col] == 'Q'){
                return false;
            }
        }

        // 45度
        for(int i = row-1,j=col-1 ; i>=0 && j>=0 ;i--,j--){
            if(cheesBoard[i][j] =='Q'){
                return false;
            }
        }

        // 135 度
        for(int i = row-1,j=col+1; i>=0 && j<n;i--,j++){
            if(cheesBoard[i][j] =='Q'){
                return false;
            }
        }
        return true;
    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.println("输入n");
        int n = sc.nextInt();
        nQueens(n);
        System.out.println("结果是");
        System.out.println(res.toString());
    }
}