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Algorithms for Competitive Programming

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Home
Home
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
- 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

December 13, 2022

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