<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) {
        double _Area, minArea = 0.0;
        if (points.size() < 4){
            return 0;
        }
        int x0, y0;
        int x1, y1;
        int x2, y2;
        int x3, y3;
        int Lx1, Ly1;
        int Lx2, Ly2;
        for(int i = 0; i < points.size() - 3; i ++){

            x0 = points[i][0];
            y0 = points[i][1];

            for (int j = i + 1; j < points.size(); j ++){
                x1 = points[j][0];
                y1 = points[j][1];
                for (int k = j + 1; k < points.size(); k ++){
                    x2 = points[k][0];
                    y2 = points[k][1];

                    Lx1 = x1 - x0;
                    Ly1 = y1 - y0;
                    
                    Lx2 = x2 - x0;
                    Ly2 = y2 - y0;

                    int dotProd = Lx1 * Lx2 + Ly1 * Ly2;
                    if (dotProd != 0){
                        continue;
                    }
                    bool skip = true;
                    for (int n = 0; n < points.size(); n ++){
                        x3 = points[n][0];
                        y3 = points[n][1];
                        if ((x3 == x0 + Lx1 + Lx2) && (y3 == y0 + Ly1 + Ly2)){
                            skip = false;
                            break;
                        }
                    }
                    if(skip == true){
                        continue;
                    }
                    _Area = (double)abs(Lx1 * Ly2 - Ly1 * Lx2);

                    if (minArea == 0.0){
                        minArea = _Area; 
                    }else{
                        minArea = minArea < _Area ? minArea : _Area;
                    }
                }
            }
        }
        return minArea;
    }
};
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