<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) {
        unordered_map<int, unordered_set<int>> s;
        for(auto p: points) {
            s[p[0]].insert(p[1]);
        }
        double minArea = DBL_MAX;
        for(int i =0; i<points.size(); i++) {
            int xi = points[i][0], yi = points[i][1];
            for(int j = i+1; j<points.size(); j++) {
                int xj = points[j][0], yj = points[j][1];
                for(int k = j+1; k<points.size(); k++) {
                    int xk = points[k][0], yk = points[k][1];
                    if(((xj-xi)*(xk-xi) + (yj - yi)*(yk - yi)) == 0) { // 2 lines perpendicular
                        int xm = xj+xk-xi;
                        int ym = yj+yk-yi;
                        if(s[xm].find(ym) != s[xm].end()) {
                            double area = sqrt(pow(xk - xi,2) + pow(yk - yi,2)) * sqrt(pow(xj-xi,2) + pow(yj - yi,2));
                            if(area < minArea) minArea = area;
                        }
                    }
                }
            }
        }
        return minArea == DBL_MAX ? 0: minArea;
    }
};
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