<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) {
        int n=points.size();
        unordered_map<string,vector<vector<int>>>mp;
        for(int i=0;i<n;i++){
            for(int j=i+1;j<n;j++){
                string s="";
                double midx=((double)(points[i][0]+points[j][0]))/((double)2);
                double midy=((double)(points[i][1]+points[j][1]))/((double)2);
                double l= ((points[i][0]-points[j][0])*(points[i][0]-points[j][0])) + ((points[i][1]-points[j][1]) * (points[i][1]-points[j][1]));
                s=to_string(midx)+to_string(midy)+to_string(l);
                mp[s].push_back({i,j});
            }
        }
        double ans=(double)INT_MAX;
        for(auto it:mp){
            vector<vector<int>>pair=it.second;
            if(pair.size()<2)
            continue;
            for(int i=0;i<pair.size();i++){
                for(int j=i+1;j<pair.size();j++){
                    int p1=pair[i][0];
                    int p2=pair[i][1];
                    int p3=pair[j][0];
                    int p4=pair[j][1];
                    double area = sqrt((points[p1][0] - points[p3][0]) * (points[p1][0] - points[p3][0]) +
                   (points[p1][1] - points[p3][1]) * (points[p1][1] - points[p3][1])) *
                    sqrt((points[p2][0] - points[p3][0]) * (points[p2][0] - points[p3][0]) +
                   (points[p2][1] - points[p3][1]) * (points[p2][1] - points[p3][1]));
                   if(area>0)
                   ans=min(ans,area);
                }
            }
        }
        return ans == (double)INT_MAX ? 0 : ans;
    }
};
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