<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:
    int eps = pow(10, -5);

    double minAreaFreeRect(vector<vector<int>>& points) {
        unordered_map<double, unordered_map<double, unordered_map<double, vector<pair<int,int>>>>> cCache;
        double dy, dx, cy, cx, dist, slope, res = INT_MAX;;
        int n = points.size(), leftX, leftY;
        for (unsigned int i = 0; i < n; ++i) {
            for (unsigned int j = i+1; j < n; ++j) {
                // Store center point
                dy = points[i][1] - points[j][1];
                dx = points[i][0] - points[j][0];
                cy = (abs(dy) / 2.0) + min(points[i][1], points[j][1]);
                cx = (abs(dx) / 2.0) + min(points[i][0], points[j][0]);
                dist = sqrt(pow(dy, 2) + pow(dx, 2));

                cout << dy << " " << dx << " " << cy << " " << cx << " " << dist << endl;
                
                if (points[i][0] < points[j][0]) {
                    leftX = points[i][0];
                    leftY = points[i][1];
                } else {
                    leftX = points[j][0];
                    leftY = points[j][1];
                }

                const vector<pair<int,int>>& val = cCache[cx][cy][dist];
                for (unsigned int i = 0; i < val.size(); ++i) {
                    double h = sqrt(pow(leftX - val[i].first, 2) + pow(leftY - val[i].second, 2));
                    double w = sqrt(pow(dist, 2) - pow(h, 2));
                    res = min(res, h*w);
                }
                // Store left-most point
                cCache[cx][cy][dist].push_back({leftX, leftY});
            }
        }
        return res == INT_MAX ? 0 : res;
    }
};
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