<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();

        // Hashmap to hold the collection of y-vertices for each x vertex
        unordered_map< int, set< int > > hashMap;
        int minX = INT_MAX, maxX = INT_MIN;
        for( const auto& point : points ) {
            hashMap[ point[ 0 ] ].insert( point[ 1 ] );
            minX = min( minX, point[ 0 ] );
            maxX = max( maxX, point[ 0 ] );
        }

        int minArea = INT_MAX;
        // Now for each x-vertex, find the y-vertices(using set intersection)
        // common to both this x-vertex and its neighbouring x-vertices
        for( int i = minX; i <= maxX; i++ ) {
            if( hashMap.find( i ) == hashMap.end() ) {
                continue;
            }
            for( int j = i+1; j <= maxX; j++ ) {
                if( hashMap.find( j ) == hashMap.end() ) {
                    continue;
                }
                int length = j - i;
                set<int> intersection;
                set_intersection( hashMap[i].begin(), hashMap[i].end(),
                                  hashMap[j].begin(), hashMap[j].end(),
                                  inserter( intersection,
                                            intersection.begin() ) );
                if( intersection.empty() || intersection.size() < 2 ) {
                    // empty: No common y-axis b/w the two x-vertices, continue
                    // size < 2: no edge can be constructed
                    continue;
                }
                vector<int> vec( intersection.begin(), intersection.end() );
                // If the intersection is [ 1,3,4 ], we need to consider[3,4]
                // for the rectangle to have minimum width
                // Find the pair with minimum difference
                int minWidth = INT_MAX;
                for( int k = 1; k < vec.size(); k++ ) {
                    minWidth = min( minWidth, vec[ k ]-vec[ k-1 ] );
                }
                int area = length * minWidth;
                minArea = min( minArea, area );
            }
        }

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