Rectangle Area: Sweep Line

Sweep a vertical line from left to right. At each event:

$1.$ Rectangle start (left edge): add its $y$-interval to active set

$2.$ Rectangle end (right edge): remove its $y$-interval from active set

Between consecutive events, the covered area is: (distance to next event) $\times$ (total covered $y$-length). Use a segment tree with lazy propagation to track the covered $y$-length as intervals are added/removed. Time: $O(n \log n)$. Space: $O(n)$.