Minimum Area Rectangle - Insight

For a rectangle with sides parallel to axes, if you know two diagonal corners $(x_1, y_1)$ and $(x_2, y_2)$, the other two corners must be $(x_1, y_2)$ and $(x_2, y_1)$.

Store all points in a set for $O(1)$ lookup. For each pair of points that could be diagonal corners (different $x$ and $y$), check if the other two corners exist.

The area of the rectangle is $|x_2 - x_1| \times |y_2 - y_1|$. Track the minimum area found.