<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>>& points) {
        unordered_map<int, unordered_set<int>> m;
        for(auto p : points) {
            int x = p[0];
            int y = p[1];
            auto mit = m.find(x);
            if(mit == m.end()) {
                auto r = m.emplace(make_pair(x, unordered_set<int>{}));
                mit = r.first;
            }
            mit->second.emplace(y);
        }
        int size = points.size();

        // maxsize = 40,000 ^2 = 1,600,000,000
        int initial = 2000000000;
        int minsize = initial;
        for(int i = 0 ; i < size ; i++) {
            auto pi = points[i];
            for(int j = i+1 ; j < size ; j++) {
                auto pj = points[j];

                int x1 = pi[0];
                int y1 = pi[1];
                int x2 = pj[0];
                int y2 = pj[1];
                if((x1 != x2) && (y1 != y2)) {
                    auto mit1 = m.find(x1);
                    auto mit2 = m.find(x2);
                    auto yit2 = mit1->second.contains(y2);
                    auto yit1 = mit2->second.contains(y1);
                    if(yit2 && yit1) {
                        int size = abs(x1-x2) * abs(y1-y2);
                        if(size < minsize) {
                            minsize = size;
                        }
                    }
                }
            }
        }
        if(minsize < initial) {
            return minsize;
        } else {
            return 0;
        }
    }
};
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