<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 len = points.size();
        double res = numeric_limits<double>::max();
        if (len < 4) return 0.0;
        
        unordered_map<string, vector<pair<int, int>>> map;
        
        for (int i = 0; i < len; i++) {
            for (int j = i + 1; j < len; j++) {
                long dis = (points[i][0] - points[j][0]) * (points[i][0] - points[j][0]) + 
                           (points[i][1] - points[j][1]) * (points[i][1] - points[j][1]);
                double centerX = (points[j][0] + points[i][0]) / 2.0;
                double centerY = (points[j][1] + points[i][1]) / 2.0;
                
                ostringstream oss;
                oss << dis << "+" << centerX << "+" << centerY;
                string key = oss.str();
                
                map[key].emplace_back(i, j);
            }
        }
        
        for (const auto& entry : map) {
            if (entry.second.size() > 1) {
                const auto& list = entry.second;
                for (int i = 0; i < list.size(); i++) {
                    for (int j = i + 1; j < list.size(); j++) {
                        int p1 = list[i].first;
                        int p2 = list[j].first;
                        int p3 = list[j].second;
                        
                        double len1 = sqrt(pow(points[p1][0] - points[p2][0], 2) + 
                                           pow(points[p1][1] - points[p2][1], 2));
                        double len2 = sqrt(pow(points[p1][0] - points[p3][0], 2) + 
                                           pow(points[p1][1] - points[p3][1], 2));
                        double area = len1 * len2;
                        res = min(res, area);
                    }
                }
            }
        }
        
        return res == numeric_limits<double>::max() ? 0.0 : res;
    }
};
49674