<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 {

    bool isSafe(vector<string> positions, int row, int col) {
        
        for (int i = row-1; i >= 0; i--) {
            // same col
            if (positions[i][col] == 'Q')    return false;

            // right diagonal
            if (col+(row-i) < positions[0].length() && positions[i][col+(row-i)] == 'Q')  return false;

            if (col-(row-i) >= 0 && positions[i][col-(row-i)] == 'Q')    return false;
        }

        return true;
    }

    void helperRec(int n, int row, vector<vector<string>>& ans, vector<string>& positions) {
        if (row == n) {
            ans.push_back(positions);
            return;
        }

        string temp(n, '.');
        for (int i = 0; i < n; i++) {
            if (isSafe(positions, row, i)) {
                temp[i] = 'Q';
                positions.push_back(temp);
                helperRec(n, row+1, ans, positions);
                positions.pop_back();
                temp[i] = '.';
            }
        }
    }

public:
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<string> aSolution;

        helperRec(n, 0, ans, aSolution);

        return ans;

    }
};
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