<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:
    class Item{
    public:
        Item(int x,int y,long long len):mx(x) , my(y) , mLen(len){}
        const int mx;
        const int my;
        const long long mLen;
    };
    struct CompItem{
        bool operator()(const Item* a,const Item* b) const{
            if(a->mLen == b->mLen){
                if(a->mx == b->mx){
                    return a->my <  b->my;
                }
                return a->mx < b->mx;
            }
            return a->mLen < b->mLen;
        }
    };

    class Point{
    public:
        Point(int idx, const vector<vector<int>>& pointList){
            mx = pointList[idx][0];
            my = pointList[idx][1];
            for(int i = 0;i < pointList.size();++i){
                if(i == idx)
                    continue;
                auto & pos = pointList[i];
                int x = pos[0];
                int y = pos[1];
                long long dis = (x-mx)*(x-mx) + (y-my)*(y-my);
                mItemList.push_back(new Item(x,y,dis));
            }
            sort(mItemList.begin() , mItemList.end() , CompItem());
        }
        double ans(){
            double ret = -1;
            for(int i = 0;i < mItemList.size(); ++i){
                long long a = mItemList[i]->mLen;
                for(int j = i+1;j < mItemList.size(); ++j){
                    long long b = mItemList[j]->mLen;
                    long long tmpx = (mItemList[i]->mx + mItemList[j]->mx - 2*mx);
                    long long tmpy = (mItemList[i]->my + mItemList[j]->my - 2*my);
                    if(tmpx*tmpx +  tmpy*tmpy != a+b)
                        continue;
                    Item tmp(0,0,a+b);

                    auto it = lower_bound(mItemList.begin(),mItemList.end(),&tmp,CompItem());
                    if(it == mItemList.end()){
                        break;
                    }
                    if((*it)->mLen != (a+b))
                        continue;
                    long long tx = ((*it)->mx - mx);
                    long long ty = ((*it)->my - my);
                    if(tx != tmpx || ty != tmpy)
                        continue;
                    if(ret < 0){
                        ret = sqrt(a) * sqrt(b);
                    }
                    else{
                        ret = min(ret, sqrt(a) * sqrt(b));
                    }
                }
            }
            return ret;
        }
        int mx;
        int my;
        vector<Item*> mItemList;
    };
    double minAreaFreeRect(vector<vector<int>>& pointList) {
        map<long long,vector<pair<int,int>>> m;
        double ret = -1;
        for(int i = 0;i < pointList.size(); ++i){
            auto * point = new Point(i,pointList);
            auto res = point->ans();
            if(res < 0){
                continue;
            }
            if(ret < 0 || ret > res)
                ret = res;
        }
        if(ret < 0) return 0;
        return ret;
    }
};
17059