Last update: June 19, 2024 

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• Algebra
  • Fundamentals
    • Binary Exponentiation
    • Euclidean algorithm for computing the greatest common divisor
    • Extended Euclidean Algorithm
    • Linear Diophantine Equations
    • Fibonacci Numbers
  • Prime numbers
    • Sieve of Eratosthenes
    • Linear Sieve
    • Primality tests
    • Integer factorization
  • Number-theoretic functions
    • Euler's totient function
    • Number of divisors / sum of divisors
  • Modular arithmetic
    • Modular Inverse
    • Linear Congruence Equation
    • Chinese Remainder Theorem
    • Garner's Algorithm
    • Factorial modulo p
    • Discrete Log
    • Primitive Root
    • Discrete Root
    • Montgomery Multiplication
  • Number systems
    • Balanced Ternary
    • Gray code
  • Miscellaneous
    • Bit manipulation
    • Enumerating submasks of a bitmask
    • Arbitrary-Precision Arithmetic
    • Fast Fourier transform
    • Operations on polynomials and series
    • Continued fractions
    • Factoring Exponentiation
• Data Structures
  • Fundamentals
    • Minimum Stack / Minimum Queue
    • Sparse Table
  • Trees
    • Disjoint Set Union
    • Fenwick Tree
    • Sqrt Decomposition
    • Segment Tree
    • Treap
    • Sqrt Tree
    • Randomized Heap
  • Advanced
    • Deleting from a data structure in O(T(n) log n)
• Dynamic Programming
  • Introduction to Dynamic Programming
  • Knapsack Problem
  • DP optimizations
    • Divide and Conquer DP
    • Knuth's Optimization
  • Tasks
    • Dynamic Programming on Broken Profile. Problem "Parquet"
    • Finding the largest zero submatrix
• String Processing
  • Fundamentals
    • String Hashing
    • Rabin-Karp for String Matching
    • Prefix function - Knuth-Morris-Pratt
    • Z-function
    • Suffix Array
    • Aho-Corasick algorithm
  • Advanced
    • Suffix Tree
    • Suffix Automaton
    • Lyndon factorization
  • Tasks
    • Expression parsing
    • Manacher's Algorithm - Finding all sub-palindromes in O(N)
    • Finding repetitions
• Linear Algebra
  • Matrices
    • Gauss & System of Linear Equations
    • Gauss & Determinant
    • Kraut & Determinant
    • Rank of a matrix
• Combinatorics
  • Fundamentals
    • Finding Power of Factorial Divisor
    • Binomial Coefficients
    • Catalan Numbers
  • Techniques
    • The Inclusion-Exclusion Principle
    • Burnside's lemma / Pólya enumeration theorem
    • Stars and bars
    • Generating all K-combinations
  • Tasks
    • Placing Bishops on a Chessboard
    • Balanced bracket sequences
    • Counting labeled graphs
• Numerical Methods
  • Search
    • Binary Search
    • Ternary Search
    • Newton's method for finding roots
  • Integration
    • Integration by Simpson's formula
• Geometry
  • Elementary operations
    • Basic Geometry
    • Finding the equation of a line for a segment
    • Intersection Point of Lines
    • Check if two segments intersect
    • Intersection of Segments
    • Circle-Line Intersection
    • Circle-Circle Intersection
    • Common tangents to two circles
    • Length of the union of segments
  • Polygons
    • Oriented area of a triangle
    • Area of simple polygon
    • Check if points belong to the convex polygon in O(log N)
    • Minkowski sum of convex polygons
    • Pick's Theorem - area of lattice polygons
    • Lattice points of non-lattice polygon
  • Convex hull
    • Convex hull construction
    • Convex hull trick and Li Chao tree
  • Sweep-line
    • Search for a pair of intersecting segments
  • Planar graphs
    • Finding faces of a planar graph
    • Point location in O(log N)
  • Miscellaneous
    • Finding the nearest pair of points
    • Delaunay triangulation and Voronoi diagram
    • Vertical decomposition
    • Half-plane intersection - S&I Algorithm in O(N log N)
    • Manhattan Distance
• Graphs
  • Graph traversal
    • Breadth First Search
    • Depth First Search
  • Connected components, bridges, articulations points
    • Finding Connected Components
    • Finding Bridges in O(N+M)
    • Finding Bridges Online
    • Finding Articulation Points in O(N+M)
    • Strongly Connected Components and Condensation Graph
    • Strong Orientation
  • Single-source shortest paths
    • Dijkstra - finding shortest paths from given vertex
    • Dijkstra on sparse graphs
    • Bellman-Ford - finding shortest paths with negative weights
    • 0-1 BFS
    • D´Esopo-Pape algorithm
  • All-pairs shortest paths
    • Floyd-Warshall - finding all shortest paths
    • Number of paths of fixed length / Shortest paths of fixed length
  • Spanning trees
    • Minimum Spanning Tree - Prim's Algorithm
    • Minimum Spanning Tree - Kruskal
    • Minimum Spanning Tree - Kruskal with Disjoint Set Union
    • Second best Minimum Spanning Tree - Using Kruskal and Lowest Common Ancestor
    • Kirchhoff Theorem
    • Prüfer code
  • Cycles
    • Checking a graph for acyclicity and finding a cycle in O(M)
    • Finding a Negative Cycle in the Graph
    • Eulerian Path
  • Lowest common ancestor
    • Lowest Common Ancestor
    • Lowest Common Ancestor - Binary Lifting
    • Lowest Common Ancestor - Farach-Colton and Bender algorithm
    • Solve RMQ by finding LCA
    • Lowest Common Ancestor - Tarjan's off-line algorithm
  • Flows and related problems
    • Maximum flow - Ford-Fulkerson and Edmonds-Karp
    • Maximum flow - Push-relabel algorithm
    • Maximum flow - Push-relabel algorithm improved
    • Maximum flow - Dinic's algorithm
    • Maximum flow - MPM algorithm
    • Flows with demands
    • Minimum-cost flow
    • Assignment problem
  • Matchings and related problems
    • Bipartite Graph Check
    • Kuhn's Algorithm - Maximum Bipartite Matching
    • Hungarian Algorithm
  • Miscellaneous
    • Topological Sorting
    • Edge connectivity / Vertex connectivity
    • Tree painting
    • 2-SAT
    • Heavy-light decomposition
• Miscellaneous
  • Sequences
    • RMQ task (Range Minimum Query - the smallest element in an interval)
    • Longest increasing subsequence
    • Search the subsegment with the maximum/minimum sum
    • K-th order statistic in O(N)
    • MEX task (Minimal Excluded element in an array)
  • Game Theory
    • Games on arbitrary graphs
    • Sprague-Grundy theorem. Nim
  • Schedules
    • Scheduling jobs on one machine
    • Scheduling jobs on two machines
    • Optimal schedule of jobs given their deadlines and durations
  • Miscellaneous
    • Tortoise and Hare Algorithm (Linked List cycle detection)
    • Josephus problem
    • 15 Puzzle Game: Existence Of The Solution
    • The Stern-Brocot Tree and Farey Sequences

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