<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>> solveNQueens(int n) {
        vector<vector<string>> ans;
        vector<int> loc(n,-1);//loc[i] represents the number of column that the queen at ith row situates
        solve(n,loc,0,ans);
        return ans;
    }
private:
    void solve(int n, vector<int>& loc, int row, vector<vector<string>>& ans){
        if(row==n){
            ans.push_back(loc2string(loc));
            return;
        }
        for(int col = 0 ; col < n; col++){
            if(isValidLoc(row,col,loc)){
                loc[row]=col;
                solve(n,loc,row+1,ans);
                loc[row]=-1;
            }
        }
    }
    vector<string> loc2string(vector<int> loc){
        int n = loc.size();
        vector<string> ans(n,string(n,'.'));
        for(int i =0; i < n; i++){
            ans[i][loc[i]] = 'Q';
        }
        return ans;
    }
    bool isValidLoc(int row, int col, vector<int> loc){
        for(int irow=0; irow<row;irow++){
            if(loc[irow]==col) return false;
            if(loc[irow]-col==(row-irow)) return false;
            if(loc[irow]-col==-(row-irow)) return false;
        }
        return true;
    }
};
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