<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 a rectangle formed from these points, with sides parallel to the X and Y axes</em>. If there is not any such rectangle, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec1.JPG" style="width: 500px; height: 447px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[2,2]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/rec2.JPG" style="width: 500px; height: 477px;" />
<pre>
<strong>Input:</strong> points = [[1,1],[1,3],[3,1],[3,3],[4,1],[4,3]]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= points.length &lt;= 500</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:
    int minAreaRect(vector<vector<int>>& p) {
        
        int n = p.size(), ar = INT_MAX, df;
        map<int, multiset<int>> x;
        
        sort(p.begin(), p.end());
        
        for(auto v: p)
            x[v[0]].insert(v[1]);
        
        for(auto it = x.begin(); it != x.end(); it++)
        {
            if(it->second.size() >= 2)
            {
                auto v = it->second;
                
                auto it1 = it;
                it1 ++;
                for(; it1 != x.end(); it1 ++)
                {
                    if(it1->first - it->first > ar) break;
            
                    if(it1->second.size() >=2)
                    {
                        auto u = it1->second;
                        vector<int> hd;
                        for(int i: v)
                        {
                            if(u.count(i)) hd.push_back(i);
                        }
                        if(hd.size() >=2)
                        {
                            df = hd[1] - hd[0];
                            for(int i=2; i<hd.size(); i++)
                                if(hd[i] - hd[i-1] < df) df = hd[i] - hd[i-1];
                            ar = min(ar, df * (it1->first - it->first));
                        }
                        
                    }
                }
            }
        }
        
        return ar==INT_MAX? 0: ar;
    }
};
87240