Rectangle Area II Solution

Implementation steps:

$1.$ Coordinate compress $y$-values

$2.$ Create events: $(x, \text{type}, y_1, y_2)$ for each rectangle edge

$3.$ Sort events by $x$

$4.$ Sweep: between events, add (covered length) $\times$ ($x$ difference) to area

$5.$ Update segment tree for the current event

The segment tree tracks how much of each $y$-segment is covered. Nodes store cover count; query returns total covered length. This is an advanced problem combining sweep line, coordinate compression, and segment trees. Time: $O(n \log n)$. Space: $O(n)$.