<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 {
public:
    double minAreaFreeRect(vector<vector<int>>& points) {
        if (points.size() < 4) return 0.0;
        unordered_map<string, vector<vector<int>>> m;
        int n = points.size();
        for (int i = 0; i < n; i++)
        {
            for (int j = i+1; j < n; j++)
            {
                long dist = get_dist(points[i], points[j]);
                double center_x = (points[i][0] + points[j][0]) / 2.0;
                double center_y = (points[i][1] + points[j][1]) / 2.0;
                string key = to_string(dist) + "_" + to_string(center_x) + "_" + to_string(center_y);
                m[key].push_back({i, j});
            }
        }

        double res = DBL_MAX;
        for (auto element: m)
        {
            vector<vector<int>> pts = element.second;
            if (pts.size() < 2) continue;
            for (int i = 0; i < pts.size(); i++)
            {
                for (int j = i+1; j < pts.size(); j++)
                {
                    int p0 = pts[i][0];
                    int p1 = pts[j][0];
                    int p2 = pts[j][1];
                    double wid = sqrt(get_dist(points[p0], points[p1]));
                    double len = sqrt(get_dist(points[p0], points[p2]));
                    res = min(res, wid*len);
                }
            }
        }
        return res == DBL_MAX ? 0.0 : res;
    }
    long get_dist(vector<int> p1, vector<int> p2)
    {
        double diff_x = p1[0] - p2[0];
        double diff_y = p1[1] - p2[1];
        return diff_x * diff_x + diff_y * diff_y;
    }
};
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