<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) {
        int n = points.size();
        if (n < 4) return 0.0;
        double res = DBL_MAX;
        unordered_map<string, vector<vector<int>>> m;
        for (int i = 0; i < n; ++i) {
            for (int j = i + 1; j < n; ++j) {
                long dist = getLength(points[i], points[j]);
                double centerX = (points[i][0] + points[j][0]) / 2.0;
                double centerY = (points[i][1] + points[j][1]) / 2.0;
                string key = to_string(dist) + "_" + to_string(centerX) + "_" + to_string(centerY);
                m[key].push_back({i, j});
            }
        }
        for (auto &a : m) {
            vector<vector<int>> vec = a.second;
            if (vec.size() < 2) continue;
            for (int i = 0; i < vec.size(); ++i) {
                for (int j = i + 1; j < vec.size(); ++j) {
                    int p1 = vec[i][0], p2 = vec[j][0], p3 = vec[j][1];
                    double len1 = sqrt(getLength(points[p1], points[p2]));
                    double len2 = sqrt(getLength(points[p1], points[p3]));
                    res = min(res, len1 * len2);
                }
            }
        }
        return res == DBL_MAX ? 0.0 : res;
    }
    
    long getLength(vector<int>& pt1, vector<int>& pt2) {
        return (pt1[0] - pt2[0]) * (pt1[0] - pt2[0]) + (pt1[1] - pt2[1]) * (pt1[1] - pt2[1]);
    }
};
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