<p>The <strong>n-queens</strong> puzzle is the problem of placing <code>n</code> queens on an <code>n x n</code> chessboard such that no two queens attack each other.</p>

<p>Given an integer <code>n</code>, return <em>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/11/13/queens.jpg" style="width: 600px; height: 268px;" />
<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
    int totalNQueens(int n) {
        vector<vector<string>> ans;
        vector<string> board(n);
        string s(n,'.');
        for(int i=0;i<n;i++)
            board[i] = s;
        solve(0,ans,board,n);
        return ans.size();
    }
    void solve(int col, vector<vector<string>> &ans, vector<string> &board, int n){
        if(col == n){
            ans.push_back(board);
            return;
        }
        for(int row=0;row<n;row++){
            if(safe(row,col,board,n)){
                board[row][col] = 'Q';
                solve(col+1,ans,board,n);
                board[row][col] = '.';
            }
        }
    }
    bool safe(int row, int col, vector<string> &board, int n){
        int dupcol = col;
        int duprow = row;
        while(col >= 0 && row >=0){
            if(board[row][col] == 'Q') return false;
            col--;
            row--;
        }
        row = duprow;
        col = dupcol;
        while(col >= 0){
            if(board[row][col] == 'Q') return false;
            col--;
        }
        row = duprow;
        col = dupcol;
        while(row < n && col >= 0){
            if(board[row][col] == 'Q') return false;
            row++;
            col--;
        }
        return true;
    }
};
8387