<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 getDist2(vector<int>& p1, vector<int>& p2){
        return (p1[0] - p2[0]) * (p1[0] - p2[0]) + (p1[1] - p2[1]) * (p1[1] - p2[1]);
    }
    double minAreaFreeRect(vector<vector<int>>& points) {
        int n = points.size();
        double ans = DBL_MAX, area = DBL_MAX;
        for(int i=0; i<n-3; i++){
            for(int j=i+1; j<n-2; j++){
                for(int k=j+1; k<n-1; k++){
                    for(int l=k+1; l<n; l++){
                        // check rectangle properties
                        double ij = getDist2(points[i], points[j]);
                        double ik = getDist2(points[i], points[k]);
                        double il = getDist2(points[i], points[l]);
                        double jk = getDist2(points[j], points[k]);
                        double jl = getDist2(points[j], points[l]);
                        double kl = getDist2(points[k], points[l]);

                        // i     j 
                        // k     l
                        if(ij + ik == il && ij == kl && ik == jl && il == jk){
                            area = sqrt(ij) * sqrt(ik);
                            ans = min(ans, area);
                        }// i     l
                        // k     j
                        else if(il + ik == ij && il == jk && ik == jl && ij == kl){
                            area = sqrt(il) * sqrt(ik);
                            ans = min(ans, area);
                        }// i     j
                        // l     k
                        else if(ij + il == ik && ij == kl && il == jk && ik == jl){
                            area = sqrt(ij) * sqrt(il);
                            ans = min(ans, area);
                        }
        
                    }
                }
            }
        }
        return ans == DBL_MAX ? 0 : ans;
    }
};
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