<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 {
    typedef vector<string> board;

    void solve(vector<board> &b, board &state, vector<bool> &row, vector<bool> &d1, vector<bool> &d2, int n, int t) {
        if(n == t) {
            cout << "done\n";
            b.push_back(state);
            return;
        }

        for(int i = 0; i < t; i++) {
            if(!row[i] && !d1[t - 1 + i - n] && !d2[n + i]) {
                row[i] = true;
                d1[t - 1 + i - n] = true;
                d2[n + i] = true;
                state[n][i] = 'Q';

                solve(b, state, row, d1, d2, n + 1, t);

                row[i] = false;
                d1[t - 1 + i - n] = false;
                d2[n + i] = false;
                state[n][i] = '.';
            }
        }
    }

public:
    vector<vector<string>> solveNQueens(int n) {
        vector<board> boards;
        board state(n, string(n, '.'));
        vector<bool> row(n, false), d1(2 * n - 1, false), d2(2 * n - 1, false);

        solve(boards, state, row, d1, d2, 0, n);

        return boards;
    }
};
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