<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

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

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

class Solution {
    vector<vector<string>> res;

    bool isSafe(const vector<string>& board, int row, int col) {
        for (int i = 0; i < row; i++) 
            if (board[i][col] == 'Q')
                return false;

        for (int i = row, j = col; i >= 0 && j >= 0; i--, j--)
            if (board[i][j] == 'Q')
                return false;

        for (int i = row, j = col; i >= 0 && j < board.size(); i--, j++)
            if (board[i][j] == 'Q')
                return false;

        return true;
    }

    vector<int> getPossibilities(const vector<string>& board, int row) {
        vector<int> cols;

        for(int col=0; col<board.size(); ++col)
            if(isSafe(board, row, col))
                cols.push_back(col);

        return cols;
    }
    
    void solveNQueensRec(vector<string> board, int row) {
        if(row == board.size()){
            res.push_back(board);
            return;
        }

        vector<int> possibilities = getPossibilities(board, row);

        for(int i=0; i < possibilities.size(); ++i){
            board[row][possibilities[i]] = 'Q';
            solveNQueensRec(board, row + 1);
            board[row][possibilities[i]] = '.';
        }
    }

public:
    vector<vector<string>> solveNQueens(int n) {
        string dashes(n, '.');
        vector<string> board(n, dashes);

        solveNQueensRec(board, 0);

        return res;
    }
};
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