<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:
    void placeQueen(vector<vector<int>>& table, int n, int r, int c) {
        for (int i=0; i<n; i++) {
            table[r][i] = 1;
            table[i][c] = 1;
            if (r+i<n && c+i<n)
                table[r+i][c+i] = 1;
            if (r+i<n && c-i>=0)
                table[r+i][c-i] = 1;
            if (r-i>=0 && c+i<n)
                table[r-i][c+i] = 1;
            if (r-i>=0 && c-i>=0)
                table[r-i][c-i] = 1;
        }
        table[r][c] = 2;
    }
    void pushAns(vector<vector<int>> table, vector<vector<string>>& ret) {
        vector<string> ds;
        int n = table.size();
        for (int r=0; r<n; r++) {
            string row = "";
            for (int c=0; c<n; c++) {
                if (table[r][c] == 2)
                    row += "Q";
                else
                    row += ".";
            }
            ds.push_back(row);
        }
        ret.push_back(ds);
    }
    void backTracking(vector<vector<int>>& table, vector<vector<string>>& ret, int n, int ind) {
        if (ind == n) {
            pushAns(table, ret);
            cout << "push\n";
            return;
        }
        for (int i=0; i<n; i++) {
            if (table[ind][i] == 0) {
                vector<vector<int>> rep = table;
                placeQueen(rep, n, ind, i);
                backTracking(rep, ret, n, ind+1);
            }
        }
        return;
    }
    vector<vector<string>> solveNQueens(int n) {
        vector<vector<int>> table(n, vector<int> (n, 0));
        vector<vector<string>> ret;
        backTracking(table, ret, n, 0);
        return ret;
    }
};

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