<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 dist(int x1, int y1, int x2, int y2){
        int sum = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2);
        return sqrt((double)sum);
    }

    double minAreaFreeRect(vector<vector<int>>& points) {
        map<vector<int>, vector<vector<int>> > centreToPoints; // cx,cy,diagonal len->x1,y1,x2,y2
        int pointCnt = points.size();
        for(int i=0; i<pointCnt; i++){
            for(int j=i+1; j<pointCnt; j++){
                int x1 = points[i][0];
                int y1 = points[i][1];
                int x2 = points[j][0];
                int y2 = points[j][1];

                int cx = (x1 + x2); // centre x * 2 being stored
                int cy = (y1 + y2); // centre y * 2 being stored
                int diagonal = (x1-x2)*(x1-x2) + (y1-y2)*(y1-y2); // store square of diagonal
                centreToPoints[{cx,cy,diagonal}].push_back({x1,y1,x2,y2});
            }
        }

        double area = 100000000000;

        for(auto &[centreDiag,points] : centreToPoints){
            if(points.size() <= 1) continue;
            // Calc area for all pairs of points
            for(int i=0; i<points.size(); i++){
                for(int j=i+1; j<points.size(); j++){
                    int p1x = points[i][0];
                    int p1y = points[i][1];
                    int p2x = points[j][0];
                    int p2y = points[j][1];
                    int p3x = points[j][2];
                    int p3y = points[j][3];
                    double side1 = dist(p1x,p1y,p2x,p2y);
                    double side2 = dist(p1x,p1y,p3x,p3y);
                    area = min(area, side1*side2);
                }
            }
        }

        if(area == 100000000000){
            return 0.0;
        }

        return area;
    }
};
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