<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:
    void solve(vector<vector<string>>& result, vector<string>board, vector<bool> diag1, vector<bool> diag2, vector<bool> cols, int row, int n) {
        if (row == n) {
            result.push_back(board);
            return;
        }
        for(int i=0;i<n;i++) {
            if(cols[i] || diag1[row-i+n-1] || diag2[row+i]) continue;
            board[row][i] = 'Q';
            cols[i] = true;
            diag1[row-i+n-1] = true;
            diag2[row+i] = true;

            solve(result, board, diag1, diag2, cols, row+1, n);
            
            board[row][i] = '.';
            cols[i] = false;
            diag1[row-i+n-1] = false;
            diag2[row+i] = false;
        }
    }
    int totalNQueens(int n) {
        vector<vector<string>> result;
        vector<string> board(n, string(n, '.'));
        vector<bool> cols(n, false);
        vector<bool> diag1(2*n-1, false);
        vector<bool> diag2(2*n-1, false);

        solve(result, board, diag1, diag2, cols, 0, n);

        return result.size();
    }

};
17657