<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 placeQ(int i, int j, int n, vector<vector<bool>>& attacked) {
        int k;
        for(k=0; k<n; k++) attacked[k][j] = true;
        for(k=0; k<n; k++) attacked[i][k] = true;
        
        k = -1*min(i,j);
        for(; max(i,j)+k<n; k++) attacked[i+k][j+k] = true;
        for(k=0; i+k<n && j-k>=0; k++) attacked[i+k][j-k] = true;
        for(k=0; i-k>=0 && j+k<n; k++) attacked[i-k][j+k] = true;
    }

    vector<vector<pair<int,int>>> backtrack(int n, int ith, vector<vector<bool>>& attacked) {
        vector<vector<pair<int,int>>> ans, t_;
        if(ith==n) return ans;

        // cout<<n<<" "<<ith<<"\n";
        // for(int i=0;i<n;i++){
        //     for(int j=0; j<n; j++)
        //         cout<<attacked[i][j]<<" ";
        //     cout<<endl;
        // }
        // cout<<endl;

        vector<vector<bool>> temp = attacked;
        int i;
        for(i=0; i<n; i++)
            if(attacked[ith][i]==false)
                break;
        if(i==n)
            return ans;
        
        for(i=0; i<n; i++)
        {
            if(attacked[ith][i]==false)
            {
                if(ith+1==n) {
                    vector<pair<int,int>> dummy;
                    dummy.push_back(make_pair(ith, i));
                    ans.push_back(dummy);
                    return ans;
                }
                temp = attacked;
                placeQ(ith, i, n, temp);
                t_ = backtrack(n, ith+1, temp);
                if(t_.size()==0)
                    continue;
                vector<pair<int,int>> dummy;
                for(int j=0; j<t_.size(); j++){
                    dummy.clear();
                    dummy.push_back(make_pair(ith, i));
                    dummy.insert(dummy.end(), t_[j].begin(), t_[j].end());
                    ans.push_back(dummy);
                }
            }
        }
        return ans;
    }

    vector<vector<string>> makestring(vector<vector<pair<int,int>>> pair_ans, int n) {
        vector<vector<string>> ans;
        vector<string> init, temp;
        string s="";
        int i;
        for(i=0; i<n; i++)
            s = s+".";
        for(i=0; i<n; i++) {
            init.push_back(s);
        }
        for(i=0; i<pair_ans.size(); i++) {
            temp = init;
            // sort(pair_ans[i].begin(), pair_ans[i].end());
            for(int j=0; j<n; j++)
                temp[pair_ans[i][j].first][pair_ans[i][j].second] = 'Q';
            ans.push_back(temp);
        }
        return ans;
    }


    vector<vector<string>> solveNQueens(int n) {
        vector<vector<bool>> attacked(n, vector<bool>(n, false));
        vector<vector<string>> ans;
        vector<vector<pair<int,int>>> pair_ans = backtrack(n,0,attacked);
        ans = makestring(pair_ans, n);
        return ans;
    }
};
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