<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(int col, vector<int>& board, vector<vector<int>>& res, vector<int>& leftRow, vector<int>& lowerDiagonal, vector<int>& upperDiagonal,int n){
        if(col==n){
            res.push_back(board);
            return;
        }
        for(int row=0;row<n;row++){
            if(leftRow[row]==0 && lowerDiagonal[col+row]==0 && upperDiagonal[n-1+col-row]==0){
                board[col]=row+1;
                leftRow[row]=1;
                lowerDiagonal[col+row]=1;
                upperDiagonal[n-1+col-row]=1;
                solve(col+1,board, res, leftRow, lowerDiagonal, upperDiagonal,n);
                leftRow[row]=0;
                lowerDiagonal[col+row]=0;
                upperDiagonal[n-1+col-row]=0;
            }
        }
    }

    int totalNQueens(int n) {
        vector<vector<int>> res;
        vector<int> board(n,0);
        vector<int> leftRow(n,0), lowerDiagonal(2*n-1,0), upperDiagonal(2*n-1,0);
        solve(0,board,res,leftRow,lowerDiagonal,upperDiagonal,n);
        return res.size();
    }
};
7872