<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, vector<int>> xMap;           // x -> i
        map<pair<int, int>, vector<int>> yMap;        // (y1, y2) -> x_min
        int i =0;
        for(auto & p : points)
        {
            xMap[p[0]].emplace_back(i);
            i++;
        }

        int area = numeric_limits<int>::max();

        for(auto & p : xMap)
        {
            auto x1 = p.first;
            auto & pts = p.second;
            int nPts = pts.size();
            for(int i=0; i<nPts; ++i)
            {
                for(int j=i+1; j<nPts; ++j)
                {
                    int y1 = points[pts[i]][1];
                    int y2 = points[pts[j]][1];
                    if(y1 > y2)
                    {
                        std::swap(y1, y2);
                    }

                    auto & vecX = yMap[{y1, y2}];
                    if(!vecX.empty())
                    {
                        int h = y2-y1;
                        int l = std::numeric_limits<int>::max();
                        for(auto & x3 : vecX)
                        {
                            l = std::min(l, abs(x3-x1));
                        }
                
                        area = std::min(area, l*h);
                    }

                    vecX.emplace_back(x1);
                }
            }
        }

        return area == numeric_limits<int>::max()? 0 : area;
    }
};
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