<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) {
        int n = points.size();
        map<pair<int, int>, set<int>> mp;
        // y1, y2 -> their x
        
        int res = INT_MAX;
        for (int i = 0; i < n; ++i)
        {
            for (int j = i + 1; j < n; ++j)
            {
                int x = points[i][0];
                if (x != points[j][0])
                    continue;
                
                int y1 = points[i][1], y2 = points[j][1];
                if (y1 > y2)
                    swap(y1, y2);
                
                auto it = mp.find({y1, y2});
                if (it != mp.end())
                {
                    int y_diff = y2 - y1;
                    auto& x_set = it->second;

                    auto next_x = x_set.lower_bound(x);
                    if (next_x != x_set.end())
                    {
                        res = min(res, y_diff * (*next_x - x));
                    }
                    
                    if (next_x != x_set.begin())
                    {
                        res = min(res, y_diff * (x - *prev(next_x)));
                    }
                }
                
                mp[{y1, y2}].insert(x);
            }
        }

        return res == INT_MAX ? 0 : res;
    }
};
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