Geometry -> Counting Geometry¶

Count intersections, lattice points, or union areas by mixing geometry primitives with combinatorics and data structures.

Microtopics¶

Source	Type
cp-algorithms Pick's theorem	`Reference`
cp-algorithms lattice points	`Reference`
USACO Guide range queries with sweep line	`Reference`

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Polygon Lattice Points	`CSES`	`Medium`	-	Counting	GCD; Shoelace Formula	Lattice Points; Pick's Theorem	A perfect counting-geometry problem on polygons.
Right Triangles	`Codeforces`	`Medium`	-	Combinatorics	Row/Column Counting	Grid Geometry; Right Triangles	A grid-counting geometry problem with a simple but elegant formula.
Satyam and Counting	`Codeforces`	`Hard`	Triangles	-	-	Points; Right-Triangles; Combinatorics	A modern CF counting-geometry task with triangle counting flavor.
Triangles 3000	`Codeforces`	`Very Hard`	Lines	-	-	Intersections; Triangle-Counting; Arrangements	A high-end geometric counting problem on line arrangements.

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Area of Rectangles	`CSES`	`Hard`	Union-Area	Coordinate Compression	Interval Counting	Area Union; Sweep Line; Measure; Events; Rectangle-Union	Area accumulation from geometric event processing.
Intersection Points	`CSES`	`Hard`	Sweep-Line	Event Counting	-	Intersection Counting; Orthogonal-Segments; Events; Counts	Counts geometric events rather than constructing explicit shapes.

Code	Title	Fit	Difficulty	Pattern	Note	Solution
`PRAVO`	Tam giác vuông	`secondary`	`medium`	count right triangles; normalized directions; perpendicular pairing	Note	Code

python3 scripts/generate_problem_catalog.py