<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:
    bool canPlace (int x, int col, vector<string>& s)
    {
        int row =x;
        int column = col;
        while ( x >= 0 && col >= 0 )
        {       
            if(s[x][col]=='Q')  return false;
            x--;
            col--;      
        }
        x= row;
        col=column;
        while ( x <  s.size() && col >= 0 ){
            
            if(s[x][col]=='Q') return false;
            x++;
            col--;
        }
        x= row;
        col=column; 
        while( col >= 0 )
        {  
            if (s[x][col]=='Q') return false;
            col--;
        }  
        return true;
    }
    
    
    void solve (int col, vector < string > s, int n , vector<vector<string>>& ans ){
        if (col == n) {
            ans.push_back(s);
            return;
        }

        for (int i = 0; i < n; i++) {
            if (canPlace(i, col, s)) {
                s[i][col] = 'Q';
                solve(col + 1, s, n, ans);
                s[i][col] = '.';
            }
        
    }
    }
    
    int NQueens(int n) {
        vector<vector<string>>ans;
        vector<string> s( n , string (n,'.') );
        solve ( 0 ,s, n,ans );
        return ans.size();
    }
    int totalNQueens(int n) {
        if(n==1)return 1;
        return NQueens(n);
    }
};
15082