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Algorithms for Competitive Programming

Algorithms for Competitive Programming

cp-algorithms/cp-algorithms

Algorithms for Competitive Programming

cp-algorithms/cp-algorithms

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Algebra Algebra
- Fundamentals Fundamentals
- Prime numbers Prime numbers
- Number-theoretic functions Number-theoretic functions
  - Euler's totient function
  - Number of divisors / sum of divisors
- Modular arithmetic Modular arithmetic
- Number systems Number systems
  - Balanced Ternary
  - Gray code
- Miscellaneous Miscellaneous
Data Structures Data Structures
- Fundamentals Fundamentals
  - Minimum Stack / Minimum Queue
  - Sparse Table
- Trees Trees
- Advanced Advanced
  - Deleting from a data structure in O(T(n) log n)
Dynamic Programming Dynamic Programming
- Introduction to Dynamic Programming
- Knapsack Problem
- Longest increasing subsequence
- DP optimizations DP optimizations
  - Divide and Conquer DP
  - Knuth's Optimization
- Tasks Tasks
  - Dynamic Programming on Broken Profile. Problem "Parquet"
  - Finding the largest zero submatrix
String Processing String Processing
- Fundamentals Fundamentals
- Advanced Advanced
- Tasks Tasks
Linear Algebra Linear Algebra
- Matrices Matrices
Combinatorics Combinatorics
- Fundamentals Fundamentals
- Techniques Techniques
- Tasks Tasks
Numerical Methods Numerical Methods
- Search Search
- Integration Integration
  - Integration by Simpson's formula
Geometry Geometry
- Elementary operations Elementary operations
- Polygons Polygons
- Convex hull Convex hull
  - Convex hull construction
  - Convex hull trick and Li Chao tree
- Sweep-line Sweep-line
  - Search for a pair of intersecting segments
- Planar graphs Planar graphs
  - Finding faces of a planar graph
  - Point location in O(log N)
- Miscellaneous Miscellaneous
Graphs Graphs
- Graph traversal Graph traversal
  - Breadth First Search
  - Depth First Search
- Connected components, bridges, articulations points Connected components, bridges, articulations points
- Single-source shortest paths Single-source shortest paths
- All-pairs shortest paths All-pairs shortest paths
  - Floyd-Warshall - finding all shortest paths
  - Number of paths of fixed length / Shortest paths of fixed length
- Spanning trees Spanning trees
- Cycles Cycles
- Lowest common ancestor Lowest common ancestor
- Flows and related problems Flows and related problems
- Matchings and related problems Matchings and related problems
- Miscellaneous Miscellaneous
Miscellaneous Miscellaneous
- Sequences Sequences
- Game Theory Game Theory
  - Games on arbitrary graphs
  - Sprague-Grundy theorem. Nim
- Schedules Schedules
- Miscellaneous Miscellaneous

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