<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 {
private:
    vector<vector<string>> result;
    void backtracking (int n, int row, vector<string>& chessboard) {
        if (row == n) {
            result.push_back(chessboard);
            return;
        }
        for (int col = 0; col < n; col++) {
            if (isvalid (row, col, n, chessboard)) {
                chessboard[row][col] = 'Q';
                backtracking (n, row + 1, chessboard);
                chessboard[row][col] = '.';
            }
        }
    }
    bool isvalid (int row, int col, int n, vector<string>& chessboard) {
        // same row
        for (int i = 0; i < row; i++)
            if (chessboard[i][col] == 'Q') return false;
        // 45 deg
        for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--)
            if (chessboard[i][j] == 'Q') return false;
        // 135 deg
        for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++)
            if (chessboard[i][j] == 'Q') return false;
        return true;
    }
public:
    vector<vector<string>> solveNQueens(int n) {
        result.clear();
        std::vector<std::string> chessboard(n, std::string(n, '.'));
        backtracking (n, 0, chessboard);
        return result;
    }
};
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