Combinatorics -> Lexicographic Enumeration

Generate, count, or skip combinatorial objects in lexicographic order using ranks, next-state transitions, and pruning.

• Topic slug: combinatorics/lexicographic-enumeration
• Tutorial page: Open tutorial
• Ladder page: Open ladder
• Repo problems currently tagged here: 1
• Repo companion pages: 0
• Curated external problems: 7

Microtopics

• next_permutation
• ranking
• unranking
• lexicographic-skip
• windowed-enumeration
• combinatorial-generation

Learning Sources

Source	Type
cppreference next_permutation	Primary
cp-algorithms generating combinations	Reference
OI Wiki enumerate	Reference

Practice Sources

Source	Type
CSES Creating Strings	Practice
CSES Problem Set	Practice

Curated External Problems

Core

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Count Order	AtCoder	Easy	Permutation Ranking	Math; Permutation	Factorials; Permutation Order	Permutations; Lexicographic Rank	The textbook k-th-permutation problem, ideal for rank/unrank practice.
Creating Strings	CSES	Easy	Multiset Permutations, Lexicographic Order	Backtracking; Enumeration	Sorting; Multisets	Duplicate Permutations; Generation; Sorting	A classic generation task that teaches lexicographic enumeration of unique strings.
C - One More aab aba baa	AtCoder	Medium	Multiset Permutations	-	-	K-Th Permutation; Duplicate Letters; Sorting	Classic k-th lexicographic permutation of a multiset string.
Permutation Order	CSES	Medium	Permutation Ranking, Lexicographic Order	Implementation; Math	Factorials	K-Th Permutation; Factoradic; Inverse Permutation Order	A direct bidirectional rank/unrank permutation problem with multiple query types.

Practice

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Creating Strings II	CSES	Medium	Multiset Permutations, Ranking And Counting, Lexicographic Combinatorics	Math; Precomputation	Multinomial Counting; Lexicographic Order	Counting Strings; Factorials; Mod Arithmetic	Useful if you want both counting and ordering over repeated characters.

Stretch

Problem	Source	Difficulty	Context	Style	Prerequisites	Tags	Why it fits
Lexicographically Smallest Permutation	AtCoder	Hard	Permutation-Cycles	Construction; Greedy	Permutations; Cycle Decomposition; Lexicographic Order	Lexicographic Order; Permutations; Cycle Decomposition	A strong advanced permutation problem where lexicographic minimization is the central goal.
Reverse and Count	AtCoder	Hard	Permutation Ranking	Construction; Combinatorics	Lexicographic Order	Lexicographic Order	A more specialized lexicographic ranking problem with a nice combinatorial twist.

Repo Problems

Code	Title	Fit	Difficulty	Pattern	Note	Solution
VOITSORT	Cây hoán vị	primary	hard	lexicographic enumeration; stack-sortability; cartesian tree view	Note	Code

Regeneration

python3 scripts/generate_problem_catalog.py