<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<string, vector<pair<int,int>>> diagMap;
        for(int i=0; i<points.size(); i++) {
            for(int j=i+1; j<points.size(); j++) {
                int xMid = points[i][0] + points[j][0];
                int yMid = points[i][1] + points[j][1];
                int length = (points[i][0] - points[j][0]) * (points[i][0] - points[j][0]) + (points[i][1] - points[j][1]) * (points[i][1] - points[j][1]);
            
                string key = to_string(length) + " " + to_string(xMid) + " " + to_string(yMid);
                diagMap[key].push_back({i, j});
            }
        }

        double ans = DBL_MAX;
        for(auto [diag, ps] : diagMap) {
            if(ps.size() <= 1) {
                continue;
            }

            for(int i=0; i<ps.size(); i++) {
                for(int j=i+1; j<ps.size(); j++) {
                    auto [i1,i2] = ps[i];
                    auto [i3,i4] = ps[j];
                    double x1 = points[i1][0], y1 = points[i1][1];
                    double x2 = points[i2][0], y2 = points[i2][1];
                    double x3 = points[i3][0], y3 = points[i3][1];

                    double area = sqrt(((x1-x3) * (x1-x3) + (y1-y3) *(y1-y3)) * ( (x3-x2) * (x3-x2) + (y3-y2) *(y3-y2)  )      );
                    ans = min(area, ans);
                }
            }
        }

        return ans == DBL_MAX? 0 : ans;
    }
};
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