<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>all distinct solutions to the <strong>n-queens puzzle</strong></em>. You may return the answer in <strong>any order</strong>.</p>

<p>Each solution contains a distinct board configuration of the n-queens&#39; placement, where <code>&#39;Q&#39;</code> and <code>&#39;.&#39;</code> both indicate a queen and an empty space, respectively.</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> [[&quot;.Q..&quot;,&quot;...Q&quot;,&quot;Q...&quot;,&quot;..Q.&quot;],[&quot;..Q.&quot;,&quot;Q...&quot;,&quot;...Q&quot;,&quot;.Q..&quot;]]
<strong>Explanation:</strong> There exist two distinct solutions to the 4-queens puzzle as shown above
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> [[&quot;Q&quot;]]
</pre>

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

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

class Solution {
public:
    string str1, str2; 
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> res; 
        vector<int> prevIndices; 
        if(n==2 || n==3) return res;

        vector<string> r; 
        for(int i=0; i<n; i++) str1+='.'; 
        str2=str1; 

        solveNQueens(n, 0, r, res, prevIndices); 
        return res; 
    }

    void solveNQueens(int n, int row, vector<string> r, vector<vector<string>>& res, vector<int>& prevIndices) {
        if(row==n) {
            res.push_back(r) ;
            return; 
        }

        string str=str1; 
        for(int i=0; i<n; i++) {
            str[i]='Q'; 
            if(prevIndices.size()==0 || isValid(prevIndices, row, i)) {
                cout <<"valid: "<< row << "," << i << endl;
                r.push_back(str); 
                prevIndices.push_back(i); 
                solveNQueens(n, row+1, r, res, prevIndices);
                prevIndices.pop_back(); 
                r.pop_back(); 
            }
            str=str1; 
        }
    }

    bool isValid(vector<int> prev, int row, int col) {
        for(int i=0; i<prev.size(); i++) {

            if(row==3 && col==2) cout << prev[i] << " "; 
            //check for same col or diagonal hit 
            if(prev[i]==col || (col>prev[i] && i-prev[i]==row-col) || (col<prev[i] && prev[i]+i==row+col)) return false; 
        }

        return true; 
    }

};
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