<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) {
        sort(points.begin(), points.end(), [&](auto& p1, auto& p2) {
            return p1[0] < p2[0] || p1[0] == p2[0] && p1[1] < p2[1];
        });

        auto x_by_y = multimap<int, int>();

        auto y_by_length = map<int, int>();

        auto prev_x = -1;

        auto ans = INT_MAX;
        for (auto& p: points) {
            auto x = p[0];
            auto y = p[1];

            auto rng = x_by_y.equal_range(y);

            if (x != prev_x) {
                y_by_length.clear();
            }

            for (auto it = rng.first; it != rng.second; ++it) {
                auto length = x - it->second;
                auto another_line = y_by_length.find(length);
                if (another_line != y_by_length.end()) {
                    ans = min(ans, length * (y - another_line->second));
                }
                y_by_length[length] = y; 
            }

            x_by_y.insert({y, x});
            prev_x = x;
        }

        if (ans == INT_MAX) return 0;

        return ans;
    }
};
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