<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:
    using pi = pair<int, int>;

    bool perp(pi p1, pi p2, pi p3) {
        // Calculate vectors v1 = p3 - p1 and v2 = p3 - p2
        int v1x = p3.first - p1.first;
        int v1y = p3.second - p1.second;
        int v2x = p3.first - p2.first;
        int v2y = p3.second - p2.second;

        // Check if the dot product is 0 (perpendicular)
        return (v1x * v2x + v1y * v2y) == 0;
    }

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

    double getArea(int a1, int b1, int a2, int b2, int x, int y) {
        return getDistance(a1, b1, x, y) * getDistance(a2, b2, x, y);
    }

    double minAreaFreeRect(vector<vector<int>>& points) {
        map<pi, vector<pair<pi, pi>>> mpp;

        for (int i = 0; i < points.size(); i++) {
            for (int j = i + 1; j < points.size(); j++) {
                int x = points[i][0] + points[j][0];
                int y = points[i][1] + points[j][1];
                mpp[{x, y}].push_back({{points[i][0], points[i][1]}, {points[j][0], points[j][1]}});
            }
        }

        double mini = numeric_limits<double>::max();

        for (auto &entry : mpp) {
            auto &vec = entry.second;
            for (int i = 0; i < vec.size(); i++) {
                for (int j = i + 1; j < vec.size(); j++) {
                    auto [p1, p2] = vec[i];
                    auto [p3, p4] = vec[j];

                    if (perp(p1, p2, p3)) {
                        double area = getArea(p1.first, p1.second, p2.first, p2.second, p3.first, p3.second);
                        mini = min(mini, area);
                    }
                }
            }
        }

        return mini == numeric_limits<double>::max() ? 0 : mini;
    }
};


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