<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();
        unordered_map<string,vector<vector<int>>> map; // collect all points that have the same center-distance
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < i; j++) {
                vector<int> p1 = points[i], p2 = points[j];
                float centerX = (p1[0] + p2[0]) / 2.0;
                float centerY = (p1[1] + p2[1]) / 2.0;
                int dist = (p1[0] - p2[0]) * (p1[0] - p2[0]) +  (p1[1] - p2[1]) * (p1[1] - p2[1]);
                string key = to_string(centerX) + to_string(centerY) + to_string(dist);
                map[key].push_back({i,j});
            }
        }
        double res = DBL_MAX;
        for (auto &[k,v] : map) {
            for (int i = 0; i < v.size(); i++) {
                for (int j = 0; j < i; j++) {
                    vector<int> pt1 = points[v[i][0]], pt2 = points[v[i][1]], pt3 = points[v[j][0]];
                    res = min(res, getLen(pt1, pt3) * getLen(pt2, pt3));
                }
            }
        }
        return res < DBL_MAX ? res : 0.0;
    }

    double getLen(vector<int> &p1, vector<int> &p2) {
        return sqrt((p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]));
    }
};
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