<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 {
    using Board = vector<string>;
public:
    vector<vector<string>> solveNQueens(int n) {
        Board board(n, string(n, '.'));
        vector<Board> Solutions;
        findSolutions(board, Solutions,0);
        return Solutions;
    }

    void findSolutions(Board &board,
                       vector<Board> &solutions,int i) {
        if(i==board.size()){
            solutions.push_back(board);
            return;
        }

        for (int j = 0; j < board[0].size(); ++j) {
            if(isValid(board,i,j,'Q')){
                board[i][j]='Q';
                findSolutions(board,solutions,i+1);
                board[i][j]='.';
            }
            // return;
        }
    }

    bool isValid(Board &board, int row, int col, char c = 'Q') {
        int n = board.size();
        for (int i = 0; i < n; ++i) {
            if (board[row][i] == c || board[i][col] == c)return false;
        }

        vector<vector<int>> dir{{1,  1},
                                {-1, 1},
                                {1,  -1},
                                {-1, -1}};
        for (int i = 0; i < 4; ++i) {
            int r = row;
            int cc = col;
            while (r >= 0 && r <= row && cc >= 0 && cc <n) {
                if (board[r][cc] == 'Q') return false;
                r += dir[i][0];
                cc += dir[i][1];
            }
        }
        return true;
    }
};
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