Concepts6
Sweepline Technique
The sweep line technique processes geometric or time-based events in sorted order and maintains an active set that reflects the current state at the sweep position.
Fix One Variable Technique
The Fix One Variable technique reduces multi-variable search problems by enumerating one variable explicitly and optimizing over the others with structure.
Offline Query Processing
Offline query processing means you collect all queries first and answer them later in a smart order that makes updates/queries cheap.
Voronoi Diagram and Delaunay
Voronoi diagrams partition the plane so each region contains points closest to one site, while the Delaunay triangulation connects sites whose Voronoi cells touch.
Rectangle Union Area
The union area of many axis-aligned rectangles can be computed efficiently using a sweep line over x and a segment tree tracking covered y-length.
Coordinate Compression
Coordinate compression replaces large, sparse, or arbitrary values with small consecutive integers while preserving relative order.