<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:
    vector<vector<string>> solveNQueens(int n) {
        vector<string> board(n, string(n, '.'));
        vector<vector<string>> ans;
        solve(0, board, ans, n); // row board ans
        return ans;
    }

    void solve(int rowIdx, vector<string> board, vector<vector<string>> &ans, int n){
        if(rowIdx >= n){
            ans.push_back(board);
            return;
        }

        for(int col = 0; col < n; col++){
            if(isValid(board, rowIdx, col)){
                board[rowIdx][col] = 'Q';
                solve(rowIdx + 1, board, ans, n);
                board[rowIdx][col] = '.';
            }
        }
    }


    bool isValid(vector<string>&board, int row, int col){
        // look upward
        for(int i = row - 1; i >= 0; i--)
            if(board[i][col] == 'Q')
                return false;
        
        // left diagonal upward
        for(int i = row - 1, j = col - 1; i >= 0 &&  j >= 0; i--, j--)
            if(board[i][j] == 'Q')
                return false;

        // right diagonal upward
        for(int i = row - 1, j = col + 1; i >= 0 && j < board.size(); i--, j++)
            if(board[i][j] == 'Q')
                return false;
        
        return true;
    }
};
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