<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:
    vector<vector<string>> sol;
    vector<string> createBoard(vector<vector<char>>& state, int n) {
        vector<string> board;
        for(int row = 0; row < n; row++) {
            string currRow(state[row].begin(), state[row].end());
            board.push_back(currRow);
        }
        return board;
    }
    void recurse(int n, int row, unordered_set<int> cols, unordered_set<int> diag, unordered_set<int> antiDiag, vector<vector<char>>& state) {
        if(row == n) {
            sol.push_back(createBoard(state, n));
            return;
        }
        for(int col = 0; col < n; col++) {
            int currDiag = row - col;
            int currAntiDiag = row + col;
            if(cols.find(col) != cols.end() || diag.find(currDiag) != diag.end() || antiDiag.find(currAntiDiag) != antiDiag.end()) {
                continue;
            }
            // do
            cols.insert(col);
            diag.insert(currDiag);
            antiDiag.insert(currAntiDiag);
            state[row][col] = 'Q';
            // recurse
            recurse(n, row + 1, cols, diag, antiDiag, state);
            // undo
            cols.erase(col);
            diag.erase(currDiag);
            antiDiag.erase(currAntiDiag);
            state[row][col] = '.';
        }
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<char>> emptyBoard(n, vector<char>(n, '.'));
        recurse(n, 0, unordered_set<int>(), unordered_set<int>(), unordered_set<int>(), emptyBoard);
        return sol;
    }
};
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