<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 getDistance(int x1, int y1, int x2, int y2) {
        double x_diff = x2 - x1, y_diff= y2 - y1;
        return sqrt(x_diff * x_diff + y_diff * y_diff);
    }
public:
    double minAreaFreeRect(vector<vector<int>>& points) {
        
        int n = points.size();
        double minArea = DBL_MAX;

        map<pair<int, pair<int, int>>, vector<vector<int>>> hash;

        for(int i=0; i<n; i++) {
            int x1 = points[i][0], y1 = points[i][1];
            for(int j=i+1; j<n; j++) {
                int x2 = points[j][0], y2 = points[j][1];
                int cx = (x1 + x2), cy = (y1 + y2);
                int d = (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1);

                if(hash.find({d, {cx, cy}}) != hash.end()) {
                    vector<vector<int>> matchedPoints = hash[{d, {cx, cy}}];

                    for(auto point: matchedPoints) {
                        int x3 = point[0], y3 = point[1];
                        minArea = min(minArea, getDistance(x1, y1, x3, y3) * getDistance(x2, y2, x3, y3));
                    }
                }
                hash[{d, {cx, cy}}].push_back(points[i]);
            }
        }
        return minArea == DBL_MAX ? 0 : minArea;
    }
};
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