<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 dist(int x1, int y1, int x2, int y2)
    {
        double x = (double)abs(x2-x1);
        double y = (double)abs(y2-y1);
        double ans = sqrt(x*x + y*y);
        return ans; 
    }

    double minAreaFreeRect(vector<vector<int>>& a) {
        int i,j,n=a.size();
        double ans = 1e9;

        map< vector<int>, vector<vector<int>> >m;

        for(i=0;i<n;i++)
        {
            for(j=i+1;j<n;j++)
            {
                int x=a[i][0]+a[j][0], y=a[i][1]+a[j][1];
                //cout<<i<<" "<<j<<" "<<x<<" "<<y<<" ; ";
                m[{x,y}].push_back({i,j});
            }
        }

        for(auto it:m)
        {
            vector<vector<int>> v = it.second;
            if(v.size()<2)continue;
            for(i=0;i<v.size();i++)
            {
                for(j=i+1;j<v.size();j++)
                {
                    int x1=a[v[i][0]][0], y1=a[v[i][0]][1];
                    int x2=a[v[i][1]][0], y2=a[v[i][1]][1];
                    int x3=a[v[j][0]][0], y3=a[v[j][0]][1];
                    int x4=a[v[j][1]][0], y4=a[v[j][1]][1];

                    int lhs = (y3-y1)*(y3-y2);
                    int rhs = -1 * (x3-x1)*(x3-x2);
                    //cout<<x1<<" "<<y1<<" , "<<x2<<" "<<y2<<" , "<<x3<<" "<<y3<<" , "<<x4<<" "<<y4<<" ; ";
                    if(lhs == rhs)
                    {
                        double area = dist(x1, y1, x3, y3)*dist(x2, y2, x3, y3);
                        ans = min(ans, area);
                    }
                }
            }
        }
        if(ans == 1e9)ans = 0;
        return ans;
    }
};
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