<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 {
        void solve(int col, int& ans, vector<string> board, vector<int> leftRow, vector<int> lowerDiagonal, vector<int> upperDiagonal, int n){
        if(col == n){
            ans++;
            return;
        }
        
        for(int row = 0; row < n; row++){
            if(leftRow[row] == 0 && lowerDiagonal[row + col] == 0 && upperDiagonal[(n - 1) + (row - col)] == 0){
                board[row][col] = 'Q';
                leftRow[row] = 1;
                lowerDiagonal[row + col] = 1;
                upperDiagonal[(n - 1) + (row - col)] = 1;
                solve(col + 1, ans, board, leftRow, lowerDiagonal, upperDiagonal, n);
                board[row][col] = '.';
                leftRow[row] = 0;
                lowerDiagonal[row + col] = 0;
                upperDiagonal[(n - 1) + (row - col)] = 0;
            }
        }
    }
public:
    int totalNQueens(int n) {
        int ans = 0;
        vector<string> board;
        string s(n, '.');
        for(int i = 0; i < n; i++){
            board.push_back(s);
        }
        vector<int> leftRow(n, 0), lowerDiagonal(2 * n - 1, 0), upperDiagonal(2 * n - 1, 0);
        solve(0, ans, board, leftRow, lowerDiagonal, upperDiagonal, n);
        return ans;
    }
};
18687