Advanced -> Matroid Intersection

Maximum-cardinality common independent set on one explicit ground set using exchange-graph augmentation and structure-aware matroid modeling.

• Topic slug: advanced/matroid-intersection
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 1
• Repo companion pages: 5
• Curated external problems: 1

Microtopics

• matroid-intersection
• exchange-graph
• augmenting-paths
• partition-matroid
• linear-matroid
• independence-oracles

Learning Sources

Source	Type
Extremal Combinatorics notes: Matroid Intersection	Reference
Codeforces Gym 102156 D - Pick Your Own Nim	Practice

Repo Companion Material

Material	Type
Matroid Intersection hot sheet	quick reference
Pick Your Own Nim note	flagship note
Optimization And Duality tutorial	compare point
XOR Basis tutorial	compare point
Template Library exact starter route	starter route

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Pick Your Own Nim	Codeforces Gym	Very Hard	Optimization	Modeling; Augmenting Path; Theory-Heavy	XOR Basis; Matching; Optimization And Duality	Partition Matroid; Linear Matroid; XOR Basis	A clean contest anchor where one choice per box forms a partition matroid and the xor-independence condition forms a linear matroid relative to Alice's fixed heaps.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
PICKYOUROWNNIM	Pick Your Own Nim	primary	very-hard	-	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py