<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 calculateArea(vector<vector<int>>& points, int a0, int a1, int b0, int b1) {
        // get the length of edge a0b1 and a0b0
        auto pa0 = points[a0], pb1 = points[b1], pb0 = points[b0];
        long long e1 = (pa0[0] - pb1[0]) * (pa0[0] - pb1[0]) + (pa0[1] - pb1[1]) * (pa0[1] - pb1[1]);
        long long e2 = (pa0[0] - pb0[0]) * (pa0[0] - pb0[0]) + (pa0[1] - pb0[1]) * (pa0[1] - pb0[1]);
        return sqrt(e1 * e2);
    }


    double minAreaFreeRect(vector<vector<int>>& points) {
        double ans = DBL_MAX;
        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 x0 = points[i][0], y0 = points[i][1];
                int x1 = points[j][0], y1 = points[j][1];

                int diag = (x0 - x1) * (x0 - x1) + (y0 - y1) * (y0 - y1);
                int sumX = x0 + x1, sumY = y0 + y1;

                string key = to_string(diag) + "_" + to_string(sumX) + "_" + to_string(sumY);
                
                diagMap[key].push_back({i, j});
            }
        }

        for(const auto &[key, ps] : diagMap) {
            if(points.size() < 2) {
                continue;
            }


            for (int i = 0; i < ps.size(); i++) {
                for (int j = i + 1; j < ps.size(); j++) {
                    double area = calculateArea(points, ps[i].first, ps[i].second, ps[j].first, ps[j].second);
                    ans = min(area, ans);
                }
            }

            // for(int i=0; i<ps.size(); i++) {
            //     for(int j=i+1; j < ps.size(); j++) {
            //         int a = ps[i].first, b = ps[i].second;
            //         int c = ps[j].first, d = ps[j].second;

            //         double x0 = points[a][0], y0 = points[a][1];
            //         double x1 = points[b][0], y1 = points[b][1];
            //         double x2 = points[c][0], y2 = points[c][1];
            //         double x3 = points[d][0], y3 = points[d][1];

            //         ans = min(ans, sqrt(((x2-x0) * (x2-x0) + (y2-y0)*(y2-y0)) * ((x1-x3)*(x1-x3) + (y1-y3)*(y1-y3)))  );
            //     }
            // }
        }     
    
        return ans == DBL_MAX? 0 : ans;
    
    }
};
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