<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:

    string getKey(double x, double y) {
        return to_string(x) + "_" + to_string(y);
    }

    double d(int x1, int y1, int x2, int y2) {
        return sqrt(pow(x1-x2,2) + pow(y1-y2,2));
    }

    pair<double, double> getMid(int x1, int y1, int x2, int y2) {
        return {(x1+x2)/2.0, (y1+y2)/2.0};
    }

    double minAreaFreeRect(vector<vector<int>>& points) {
        unordered_map<string, unordered_map<double, vector<pair<int, int>>>> mp;
        int N = points.size();
        for (int i = 0; i < N; i++) {
            int x1 = points[i][0], y1 = points[i][1];
            for (int j = i+1; j < N; j++) {
                int x2 = points[j][0], y2 = points[j][1];
                pair<double, double> mid = getMid(x1, y1, x2, y2);
                string key = getKey(mid.first, mid.second);
                double len = d(x1, y1, x2, y2);
                mp[key][len].push_back({i, j});
            }
        }
        double minArea = INT_MAX;

        for (auto& [mid,node] : mp) {
            for (auto& [len, p]: node) {
                for (int i = 0; i < p.size(); i++) {
                    int x1 = points[p[i].first][0], y1 = points[p[i].first][1];
                    int x2 = points[p[i].second][0], y2 = points[p[i].second][1];
                    for (int j = i+1; j < p.size(); j++) {
                        int x3 = points[p[j].second][0], y3 = points[p[j].second][1];
                        minArea = min(minArea, (d(x3, y3, x2, y2)*d(x1,y1,x3,y3)));
                    }
                }
            }
        }

        return minArea == INT_MAX ? 0 : minArea;
    }
};

/*

1. 

*/
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