<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>> isSolution(vector<vector<int>> &board, vector<vector<string>> &ans, int n) {
        vector<string> temp;
        for(int i = 0; i < n; i++) {
            string s;
            for(int j = 0; j < n; j++) {
                if(board[i][j] == 1) {
                    s += 'Q';
                } else {
                    s += '.';
                }
            }
            temp.push_back(s);
        }
        ans.push_back(temp);
        return ans;
    }

    bool isSafe(int row, int col, vector<vector<int>> &board, int n) {
        int x = row;
        int y = col;
        
        // Check same row
        while(y >= 0) {
            if(board[x][y] == 1) {
                return false;
            }
            y--;
        }

        // Check upper diagonal on left side
        x = row; 
        y = col;
        while(x >= 0 && y >= 0) {
            if(board[x][y] == 1) {
                return false;
            }
            x--;
            y--;
        }

        // Check lower diagonal on left side
        x = row; 
        y = col;
        while(x < n && y >= 0) {
            if(board[x][y] == 1) {
                return false;
            }
            x++;
            y--;
        }

        return true;
    }

    void solve(int col, vector<vector<string>> &ans, vector<vector<int>> &board, int n) {
        // Base case: If all queens are placed
        if(col == n) {
            isSolution(board, ans, n);
            return;
        }

        // Consider this column and try placing this queen in all rows one by one
        for(int row = 0; row < n; row++) {
            if(isSafe(row, col, board, n)) {
                // Place the queen
                board[row][col] = 1;
                // Recur to place rest of the queens
                solve(col + 1, ans, board, n);
                // Backtrack and remove the queen
                board[row][col] = 0;
            }
        }
    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<int>> board(n, vector<int>(n, 0));
        vector<vector<string>> ans;
        
        solve(0, ans, board, n);

        return ans;
    }
};

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