<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 is_valid(vector<string> temp, int n, int x_real, int y_real){
        int x = x_real-1;
        int y = y_real-1;

        while (x >= 0 && y >= 0){
            
            if (temp[x][y] == 'Q'){
                return false;
            }
            x--;
            y--;
        }

        x = x_real-1;
        y = y_real + 1;

        while (x >= 0 && y <= n-1){
            if (temp[x][y] == 'Q'){
                return false;
            }
            x--;
            y++;
        }
        return true;
}

    void helper_1(int n, vector<vector<string>>& possible_sol, vector<string> temp, vector<int> unusable, string dots){
        if (temp.size() == n){
            possible_sol.push_back(temp);
            return;
        }

        for (int i = 0; i < n; i++){
            if (unusable[i] == 1){
                continue;
            }
           
            dots[i] = 'Q';
            temp.push_back(dots);
            dots[i] = '.';

            if (is_valid(temp, n, temp.size()-1, i) == false){
                temp.pop_back();
                cout << "false" << endl;
                continue;
            }

            unusable[i] = 1;
            helper_1(n, possible_sol, temp, unusable, dots);
            temp.pop_back();
            unusable[i] = 0;
        }

    }

    vector<vector<string>> solveNQueens(int n) {
        vector<vector<string>> possible_sol;
        string dots;
        for (int i = 1; i <= n; i++){
            dots.push_back('.');
        }
        vector<string> temp;
        vector<int> unusable (n+1, 0);
        helper_1(n, possible_sol, temp, unusable, dots);
        return possible_sol;
    }
};
30109