Geometry -> Polygon Area And Point Location¶

Shoelace formula, point-in-polygon logic, and careful boundary handling in planar geometry.

Microtopics¶

Source	Type
cp-algorithms area of simple polygon	`Reference`
Princeton geometric primitives	`Course`
cp-algorithms point location	`Reference`

Material	Type
Geometry cheatsheet	`quick reference`
Templates overview	`template guide`

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Point Location Test	`CSES`	`Easy`	Point-Location, Orientation	Implementation	Cross Product Sign	Cross-Product; Relative-Position	A very lightweight point-location primitive useful in polygon code.
Polygon Area	`CSES`	`Easy`	Polygon-Area, Shoelace	Formula Derivation	Cross Product	Shoelace Formula; Signed-Area; Cross-Product; Simple-Polygon	A standard polygon-area starter problem.
Point in Polygon	`CSES`	`Medium`	Point-Location	Parity Counting	Orientation Test; Segment Intersection	Ray Casting; Orientation; Inside-Outside	Directly trains point-in-polygon logic and boundary handling.
Polygon Lattice Points	`CSES`	`Medium`	Polygon-Area, Lattice-Points	Counting	Shoelace Formula; GCD On Edges	Pick's Theorem; Pick-Theorem; Boundary; Interior	A classic Pick's theorem application.

Code	Title	Fit	Difficulty	Pattern	Note	Solution
`KINGDOMS`	KINGDOMS	`secondary`	`hard`	laminar regions; sweep events; containment tree	Note	Code
`POINTINPOLYGON`	Point in Polygon	`primary`	`medium`	ray casting parity; boundary classification; on segment test	Note	Code
`POLYGONAREA`	Polygon Area	`primary`	`easy`	shoelace formula; signed area accumulation; integer polygon area	Note	Code
`TFIELD`	Ruộng bậc thang	`secondary`	`hard`	nested polygons; weighted sliding window; shoelace preprocessing	Note	Code
`VOTELPH`	Bà Nà	`secondary`	`hard`	piecewise maximum; endpoint preprocessing; parabola envelopes	Note	Code

python3 scripts/generate_problem_catalog.py