一、题目

The n-queens puzzle is the problem of placing n queens on an n x n chessboard such that no two queens attack each other.

Given an integer n, return all distinct solutions to the n-queens puzzle. You may return the answer in any order.

Each solution contains a distinct board configuration of the n-queens’ placement, where ‘Q’ and ‘.’ both indicate a queen and an empty space, respectively.

Example 1:

Input: n = 4
Output: [[“.Q…”,“…Q”,“Q…”,“…Q.”],[“…Q.”,“Q…”,“…Q”,“.Q…”]]
Explanation: There exist two distinct solutions to the 4-queens puzzle as shown above
Example 2:

Input: n = 1
Output: [[“Q”]]

Constraints:

1 <= n <= 9

二、题解

class Solution {
public:vector<vector<string>> res;bool isValid(vector<string>& chessboard,int row,int col,int n){//检查列for(int i = 0;i < row;i++){if(chessboard[i][col] == 'Q') return false;}//检查45度角for(int i = row - 1,j = col - 1;i >= 0 && j >= 0;i--,j--){if(chessboard[i][j] == 'Q') return false;}//检查135度角for(int i = row - 1,j = col + 1;i >= 0 && j < n;i--,j++){if(chessboard[i][j] == 'Q') return false;}return true;}void backtracing(vector<string>& chessboard,int row,int n){if(row == n){res.push_back(chessboard);return;}for(int i = 0;i < n;i++){if(isValid(chessboard,row,i,n)){chessboard[row][i] = 'Q';backtracing(chessboard,row+1,n);chessboard[row][i] = '.';}}}vector<vector<string>> solveNQueens(int n) {vector<string> chessboard(n,string(n,'.'));backtracing(chessboard,0,n);return res;}
};