<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:
    bool isSafe1(int row, int col, vector<string> board, int n) {
        int duprow = row;
        int dupcol = col;

        while (row >= 0 && col >= 0) {
            if (board[row][col] == 'Q') return false;
            row--;
            col--;
        }

        col = dupcol;
        row = duprow;
        while (col >= 0) {
            if (board[row][col] == 'Q') return false;
            col--;
        }

        row = duprow;
        col = dupcol;
        while (row < n && col >= 0) {
            if (board[row][col] == 'Q') return false;
            row++;
            col--;
        }
        return true;
    }

    void solve(int col, vector<string>& board, vector<vector<string>>& ans, int n) {
        if (col == n) {
            ans.push_back(board);
            return;
        }
        for (int row = 0; row < n; row++) {
            if (isSafe1(row, col, board, n)) {
                board[row][col] = 'Q';
                solve(col + 1, board, ans, n);
                board[row][col] = '.';
            }
        }
    }
    
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<string> board(n);
        string s(n, '.');
         
        for (int i = 0; i < n; i++) {  //every row has a n size string
            board[i] = s;
        }
        
        solve(0, board, ans, n);
        return ans;
    }
};

// class Solution {
// public:
//     vector<vector<char>> grid;
//     vector<vector<string>> res;

//     bool canPlaceQueen(int row, int col, int n) {
//         // column check
//         for (int i = row - 1; i >= 0; i--) {
//             if (grid[i][col] == 'Q')
//                 return false;
//         }

//         // left diagonal check
//         for (int i = row - 1, j = col - 1; i >= 0 && j >= 0; i--, j--) {
//             if (grid[i][j] == 'Q')
//                 return false;
//         }

//         // right diagonal check
//         for (int i = row - 1, j = col + 1; i >= 0 && j < n; i--, j++) {
//             if (grid[i][j] == 'Q')
//                 return false;
//         }

//         return true; // no attacked
//     }

//     void f(int row, int n) {
//         if (row == n) {
//             vector<string> temp;
//             for (int i = 0; i < n; i++) {
//                 string ans = "";
//                 for (int j = 0; j < n; j++) {
//                     ans += grid[i][j];
//                 }
//                 temp.push_back(ans);
//             }
//             res.push_back(temp);
//             return;
//         }

//         for (int col = 0; col < n; col++) {
//             if (canPlaceQueen(row, col, n)) {
//                 grid[row][col] = 'Q';
//                 f(row + 1, n);
//                 grid[row][col] = '.'; // backtrack step
//             }
//         }
//     }

//     vector<vector<string>> solveNQueens(int n) {
//         grid.clear();
//         res.clear();
//         grid.resize(n, vector<char>(n, '.'));
//         f(0, n);

//         return res;
//     }
// };
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