<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 {
public:

    void addQueen(vector<string> board, int seq, int n, vector<vector<string>> &ans, int space)
    {
        if (seq == n)
        {
            ans.push_back(board);
            return;
        }
        
        if (space == n * n)
        {
            return;
        }

        int i = seq;
        {
            for (int j = 0; j < n; j++)
            {
                vector<string> tmpBoard = board;
                int tmpSpace = space;
                if (tmpBoard[i][j] == ' ')
                {
                    tmpBoard[i][j] = 'Q';
                    tmpSpace++;
                    for (int k = 0; k < n; k++)
                    {
                        if (tmpBoard[k][j] == ' ') { tmpBoard[k][j] = '.'; tmpSpace++; }
                        if (tmpBoard[i][k] == ' ') { tmpBoard[i][k] = '.'; tmpSpace++; }
                        if ((j - i) + k >= 0 && (j - i) + k < n && tmpBoard[k][(j - i) + k] == ' ') { tmpBoard[k][(j - i) + k] = '.'; tmpSpace++; }
                        if ((i + j) - k >= 0 && (i + j) - k < n && tmpBoard[(i + j) - k][k] == ' ') { tmpBoard[(i + j) - k][k] = '.'; tmpSpace++; }
                    }

                    addQueen(tmpBoard, seq + 1, n, ans, tmpSpace);
                }
            }
        }
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<string> board;
        for (int i = 0; i < n; i++)
        {
            string s;
            for (int j = 0; j < n; j++)
            {
                s.append(" ");
            }
            board.push_back(s);
        }
        addQueen(board, 0, n, ans, 0);
        return ans;
    }
};
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