<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>the number of distinct solutions to the&nbsp;<strong>n-queens puzzle</strong></em>.</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> 2
<strong>Explanation:</strong> There are two distinct solutions to the 4-queens puzzle as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 9</code></li>
</ul>

class Solution {
public:
    int totalNQueens(int n) {
        set<int> atkCols;
        set<int> pdiags;
        set<int> ndiags;
        vector<vector<char>> setup(n, vector<char>(n, '.'));
        vector<vector<string>> setups;
        generate(setups, setup, 0, atkCols, pdiags, ndiags, n);
        return setups.size();
    }

    void generate(vector<vector<string>> &setups, vector<vector<char>> &setup, int row, set<int> &atkCols, set<int> &pdiags, set<int> &ndiags, int n) {
        if (row == n) {
            vector<string> v;
            for (auto r: setup) {
                string s = "";
                for (auto c: r) {
                    s += c;
                }
                v.push_back(s);
            }
            setups.push_back(v);
            return;
        }

        for (int col = 0; col < n; col++) {
            if (atkCols.contains(col) || ndiags.contains(row - col) || pdiags.contains(row + col)) {
                continue;
            }
            atkCols.insert(col);
            ndiags.insert(row - col);
            pdiags.insert(row + col);
            setup[row][col] = 'Q';
            generate(setups, setup, row + 1, atkCols, pdiags, ndiags, n);
            setup[row][col] = '.';
            atkCols.erase(col);
            ndiags.erase(row - col);
            pdiags.erase(row + col);
        }
    }
};
14052