<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>>& v) {
        sort(v.begin(), v.end());
        double ans = DBL_MAX;
        // [cx, cy, d] -> {[x, y]}
        map<vector<double> , vector<vector<int>>> m;
        for(int i = 0; i < v.size() ; i++){
            for(int j = i + 1; j < v.size() ; j++){
                int x0 = v[i][0];
                int y0 = v[i][1];
                int x1 = v[j][0];
                int y1 = v[j][1];
                
                double cx = (x0 + x1) / 2.0;
                double cy = (y0 + y1) / 2.0;
                double dist=  sqrt((x0-x1)*(x0-x1)  + (y0-y1) * (y0-y1));

                if(m[{cx, cy, dist}].size()){
                    for(auto prevs : m[{cx, cy, dist}]){
                        int x = prevs[0];
                        int y = prevs[1];
                        double l = sqrt((x-x0)*(x-x0) + (y-y0)*(y-y0));
                        double b = sqrt((x-x1)*(x-x1) + (y-y1)*(y-y1));
                        double currArea = l * 1.0 * b;
                        if(currArea){
                            cout << l << " " << b << " " <<  currArea << '\n';
                            ans = min(ans, currArea);
                        }
                    }
                }
                m[{cx, cy, dist}].push_back({v[i][0], v[i][1]});
            }
        }
        return ans == DBL_MAX ? 0 : ans;
    }
};
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