leetcode热题100 P51 N皇后

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时间轴

时间轴

2026-03-17

init

回溯

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题目：

P51 N皇后

https://leetcode.cn/problems/n-queens/description/?envType=study-plan-v2&envId=top-100-liked

回溯：注意判断对角线时是两条对角线，方向分别为""和"/";

#include <vector>
#include <string>
#include <unordered_set>

using std::vector;
using std::string;
using std::unordered_set;

class Solution {
    private:
        unordered_set<int> uset;

        bool queen_can_stand(vector<string> &board, int n, int posi, int posj)
        {
                int i, j;

                if (uset.count(posj))
                        return false;

                // 斜角 \

                i = posi;
                j = posj;
                while (i >= 0 && j >= 0) {
                        if (board[i][j] == 'Q')
                                return false;
                        i--;
                        j--;
                }

                // 斜角 \

                i = posi;
                j = posj;
                while (i < n && j < n) {
                        if (board[i][j] == 'Q')
                                return false;
                        i++;
                        j++;
                }

                // 斜角 /

                i = posi;
                j = posj;
                while (i >= 0 && j < n) {
                        if (board[i][j] == 'Q')
                                return false;
                        i--;
                        j++;
                }

                // 斜角 /
                i = posi;
                j = posj;
                while (i < n && j >= 0) {
                        if (board[i][j] == 'Q')
                                return false;
                        i++;
                        j--;
                }

                return true;
        }
        void __solveNQueens(vector<vector<string> > &res, vector<string> &board, int n, int row)
        {
                int j;

                if (row == n) { // 最后一行已经填满
                        res.push_back(board);
                        return;
                }

                for (j = 0; j < n; j++) {
                        if (queen_can_stand(board, n, row, j)) {
                                uset.insert(j); // 标识第j列已经有皇后
                                board[row][j] = 'Q';

                                __solveNQueens(res, board, n, row + 1);

                                board[row][j] = '.';
                                uset.erase(j);
                        }
                }
        }

    public:
        vector<vector<string> > solveNQueens(int n)
        {
                int i;
                string line;
                vector<string> board;
                vector<vector<string> > res;

                for (i = 0; i < n; i++)
                        line.push_back('.');

                for (i = 0; i < n; i++)
                        board.push_back(line);

                __solveNQueens(res, board, n, 0);

                return res;
        }
};