<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) {
        map<pair<int, int>, vector<pair<int, int>>> Map;
        int N = points.size();
        double res = INT_MAX;
        for(int i=0; i<N; i++){
            for(int j=0; j<N; j++){
                if (i==j){
                    continue;
                }
                int deltaX = points[i][0]-points[j][0];
                int deltaY = points[i][1]-points[j][1];
                Map[{deltaX, deltaY}].push_back({i,j});
            }
        }
        for (auto item:Map){
            for(int m=0; m<item.second.size(); m++){
                for(int n=m+1; n<item.second.size(); n++){
                    int i = item.second[m].first;
                    int j = item.second[m].second;
                    int k = item.second[n].first;

                    int dx1 = points[i][0] - points[j][0];
                    int dy1 = points[i][1] - points[j][1];
                    int dx2 = points[i][0] - points[k][0];
                    int dy2 = points[i][1] - points[k][1];

                    if (dx1*dx2+dy1*dy2!=0){
                        continue;
                    }

                    double side1 = (points[i][0]-points[j][0])*(points[i][0]-points[j][0]) + (points[i][1]-points[j][1])*(points[i][1]-points[j][1]);
                    double side2 = (points[i][0]-points[k][0])*(points[i][0]-points[k][0]) + (points[i][1]-points[k][1])*(points[i][1]-points[k][1]);
                    double area = sqrt(side1)*sqrt(side2);
                    res = min(res, area);
                }
            }
        }
        return res==INT_MAX? 0: res;
    }
};
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