<p>You are given an array of points in the <strong>X-Y</strong> plane <code>points</code> where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>Return <em>the minimum area of any rectangle formed from these points, with sides <strong>not necessarily parallel</strong> to the X and Y axes</em>. If there is not any such rectangle, return <code>0</code>.</p>

<p>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/21/1a.png" style="width: 398px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[1,2],[2,1],[1,0],[0,1]]
<strong>Output:</strong> 2.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,2],[2,1],[1,0],[0,1], with an area of 2.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/22/2.png" style="width: 400px; height: 251px;" />
<pre>
<strong>Input:</strong> points = [[0,1],[2,1],[1,1],[1,0],[2,0]]
<strong>Output:</strong> 1.00000
<strong>Explanation:</strong> The minimum area rectangle occurs at [1,0],[1,1],[2,1],[2,0], with an area of 1.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/22/3.png" style="width: 383px; height: 400px;" />
<pre>
<strong>Input:</strong> points = [[0,3],[1,2],[3,1],[1,3],[2,1]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no possible rectangle to form from these points.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 50</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 4 * 10<sup>4</sup></code></li>
	<li>All the given points are <strong>unique</strong>.</li>
</ul>

class Solution {
    double distance(vector<int>& v1, vector<int>& v2){
        double x = (v1[0] - v2[0])*(v1[0] - v2[0]);
        double y = (v1[1] - v2[1])* (v1[1] - v2[1]);

        return x + y;
    }

    pair<double, double> center(vector<int>& v1, vector<int>& v2){
        double x = (v1[0] + v2[0]);
        double y = (v1[1] + v2[1]);

        return {x,y};
    }



public:
    double minAreaFreeRect(vector<vector<int>>& points) {
        map<string, vector<vector<int>>> center_points;

        int n = points.size();

        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                int dist = distance(points[i], points[j]);

                auto c = center(points[i], points[j]);

                string key = to_string(dist) + "," + to_string(c.first) + "," + to_string(c.second);

                center_points[key].push_back({i,j});
            }
        }

        double ans = 1e9;

        for(auto &[key, v]: center_points){
            int len = v.size();

            for(int i=0;i<len;i++){
                for(int j=i+1;j<len;j++){
                    double a = distance(points[v[i][0]], points[v[j][0]]);
                    double b = distance(points[v[i][1]], points[v[j][0]]);

                    ans = min(ans, sqrt(a*b));
                }
            }
        }

        if(ans == 1e9){
            return 0;
        }

        return ans;
    }
};
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