🍁 Base

BRANCHES

• Number Theory
• Bit Manipulation
• Mathematics
• Data Structures
• Constructive Algorithms
• Graph Theory
• Dynamic Programming
• Strings
• Numerical Methods
• Geometry
• Range Query Techniques
• Game Theory
• Scheduling
• Miscellaneous
• Polynomial / Algebra
• Randomized / Approximation
• Exact / NP‑Hard

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NAMED ALGORITHMS

• A* Algorithm
• Aho-Corasick Algorithm
• Ahuja-Orlin Algorithm
• AKS Primality Test
• Algorithm X
• Alpha-Beta Pruning
• Andrew’s Monotone Chain Algorithm
• Apostolico-Giancarlo Algorithm
• Bareiss Algorithm
• Bellman-Ford Algorithm
• Bellman-Held-Karp Algorithm
• Bentley-Ottmann Algorithm
• Bentley-Shamos Algorithm
• Berlekamp-Massey Algorithm
• Berlekamp Factorization Algorithm
• Bitap Algorithm
• Bluestein’s Algorithm
• Booth’s Algorithm
• Borůvka’s Algorithm
• Bostan-Mori Algorithm
• Bowyer-Watson Algorithm
• Boyer-Moore Algorithm
• Boyer-Myrvold Planarity Algorithm
• Brent’s Cycle Detection
• Bron-Kerbosch Algorithm
• Cantor-Zassenhaus Algorithm
• Chan’s Algorithm
• Chazelle’s MST Algorithm
• Chinese Remainder Theorem
• Christofides Algorithm
• Chu-Liu/Edmonds’ Algorithm
• Cipolla’s Algorithm
• Commentz-Walter Algorithm
• Cooley-Tukey FFT
• Cornacchia’s Algorithm
• Crochemore Algorithm
• Dancing Links
• DC3 (Skew) Algorithm
• Dijkstra’s Algorithm
• Dinic’s Algorithm
• Dobkin-Kirkpatrick Hierarchy
• Dreyfus-Wagner Algorithm
• Dutch National Flag Algorithm
• Duval’s Algorithm
• Edmonds’ Blossom Algorithm
• Edmonds-Karp Algorithm
• Eppstein’s Algorithm
• Euclidean Algorithm
• Extended Euclidean Algorithm
• Faddeev-LeVerrier Algorithm
• Farach’s Suffix Tree Algorithm
• Farach-Colton-Bender RMQ/LCA
• Fast Fourier Transform (FFT)
• Fast Walsh-Hadamard Transform (FWHT)
• Floyd’s Cycle Detection
• Floyd-Warshall Algorithm
• Ford-Fulkerson Algorithm
• Fortune’s Algorithm
• Frederickson’s MST Algorithm
• Fürer’s Algorithm
• Gabow’s SCC Algorithm
• Gabow-Edmonds Scaling Algorithm
• Gabow-Tarjan Algorithm
• Galil-Seiferas Algorithm
• Garner’s Algorithm
• Gaussian Elimination
• Goemans-Williamson Algorithm
• Goldberg-Tarjan Scaling Algorithm
• Gomory-Hu Algorithm
• Good-Thomas Algorithm
• Graham Scan
• Han’s Integer Sorting Algorithm
• Harel-Tarjan LCA Algorithm
• Held-Karp Algorithm
• Hensel Lifting
• Hierholzer’s Algorithm
• Hirschberg Algorithm
• Holm-de Lichtenberg-Thorup Dynamic Connectivity
• Hopcroft-Karp Algorithm
• Hopcroft-Tarjan Planarity Algorithm
• Gauss-Jordan Elimination
• Hu-Tucker Algorithm
• Huffman Coding
• Hungarian Algorithm
• Johnson’s Algorithm

• Kadane’s Algorithm
• Kahn’s Algorithm
• Karatsuba Algorithm
• Karger’s Algorithm
• Karger-Stein Algorithm
• Karmarkar-Karp Algorithm
• Karp’s Minimum Mean Cycle Algorithm
• Karzanov Algorithm
• Kasai Algorithm
• Kirchhoff’s Theorem
• Kirkpatrick-Seidel Algorithm
• Kitamasa Algorithm
• KMR Algorithm
• Knuth-Morris-Pratt (KMP) Algorithm
• Knuth Optimization
• Kosaraju’s Algorithm
• Kruskal’s Algorithm
• Kuhn’s Algorithm
• Lanczos Algorithm
• Lawler’s Algorithm
• Lengauer-Tarjan Algorithm
• Lenstra ECM
• Lucas Theorem
• Lucas-Lehmer Test
• Manacher’s Algorithm
• Matrix Exponentiation
• Matrix Tree Theorem
• McCreight’s Algorithm
• Mehlhorn’s LCA Algorithm
• Melkman’s Algorithm
• Micali-Vazirani Algorithm
• Miller-Rabin Primality Test
• Minimax Algorithm
• Mo’s Algorithm
• Monte Carlo Tree Search
• Montgomery Reduction
• Moore’s Voting Algorithm
• Morris Traversal
• MPM Algorithm
• Nagamochi-Ibaraki Algorithm
• Negascout
• Newton-Schulz Iteration
• Number Theoretic Transform (NTT)
• Orlin’s Maximum Flow Algorithm
• Pettie-Ramachandran MST Algorithm
• Pohlig-Hellman Algorithm
• Pollard Kangaroo Algorithm
• Pollard’s Rho Algorithm
• Prim’s Algorithm
• Proof-Number Search
• Push-Relabel Algorithm
• Quadratic Sieve
• Rabin-Karp Algorithm
• Rader’s Algorithm
• Raghavan-Thompson Randomized Rounding
• Reif’s Minimum Cut Algorithm
• SA-IS Algorithm
• Schieber-Vishkin Algorithm
• Schönhage-Strassen Algorithm
• Seidel’s LP Algorithm
• Shamos-Hoey Algorithm
• Shift-Or Algorithm
• Sieve of Eratosthenes
• Simulated Annealing
• Sleator-Tarjan Dynamic Trees
• SMAWK Algorithm
• Sprague-Grundy Theorem
• Stoer-Wagner Algorithm
• Suurballe’s Algorithm
• Tarjan’s Algorithm
• Tarjan’s Offline LCA
• Tarjan-Vishkin Algorithm
• Tonelli-Shanks Algorithm
• Toom-Cook Algorithm
• UCT (Upper Confidence Trees)
• Ukkonen’s Algorithm
• Viterbi Algorithm
• Weiner’s Algorithm
• Welzl’s Algorithm
• Wiedemann Algorithm
• Wu-Manber Algorithm
• Yao Optimization
• Yen’s Algorithm
• Z Algorithm

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DATA STRUCTURES

• 2D Fenwick Tree
• 2D Segment Tree
• AVL Tree
• B‑Tree / B+ Tree
• Binary Heap
• Binary Trie
• Binomial Heap
• Bitset
• Bitset‑based structures
• Bounding Volume Hierarchy (BVH)
• Brodal Queue
• Cartesian Tree
• Centroid Decomposition
• DAWG
• Deque
• Difference Array
• Disjoint Set Union (DSU)
• Disjoint Sparse Table
• Dynamic Segment Tree
• Dynamic Tree structures
• Eertree / Palindromic Tree
• Euler Tour Tree
• Euler tour based tree structures
• Fenwick Tree (BIT)
• Fenwick Tree on bitsets
• Fibonacci Heap
• Fusion Tree
• Heap / Priority Queue
• Heavy‑Light Decomposition (HLD)
• Hollow Heap
• Implicit Treap
• Interval Stabbing structures
• Interval Tree
• KD‑Tree
• Lazy Segment Tree
• Leftist Heap
• Li Chao Tree
• Linear Basis / XOR Basis
• Link‑Cut Tree
• Meldable Heap
• Merge Sort Tree
• Minimum Queue
• Minimum Stack
• Monotonic Queue

• Monotonic Stack
• Octree
• Ordered Set / Order Statistics Tree
• Pairing Heap
• Patricia Trie / Compressed Trie
• Persistent DSU
• Persistent Fenwick Tree
• Persistent Segment Tree
• Persistent Trie
• Policy Based Data Structures
• Prefix Sum
• Quad Tree
• Queue
• R‑Tree
• Randomized Heap
• Range Tree
• Red‑Black Tree
• Rollback DSU
• Rope / Rope Tree
• Scapegoat Tree
• Segment Tree
• Segment Tree Beats
• Segment tree for geometry sweeps
• Skew Heap
• Soft Heap
• Sparse Table
• Splay Tree
• Square Root Decomposition
• Stack
• Suffix Array
• Suffix Automaton
• Suffix Tree
• Suffix Trie
• Tango Tree
• Top Tree
• Treap
• Trie
• van Emde Boas Tree
• Versioned data structures
• Virtual Tree
• Wavelet Matrix
• Wavelet Tree
• X‑fast Trie
• Y‑fast Trie

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OUTLINE

Number Theory

• Binary Exponentiation
• Linear Diophantine Equations
• Modular Arithmetic
• Modular Inverse
• Linear Congruence
• Euler Totient Function
• Möbius Function
• Divisor Functions
• Primality Testing
• Integer Factorization
• Primitive Root
• Discrete Logarithm
• Discrete Root
• Wilson’s Theorem
• Factorial Modulo p
• Legendre Symbol
• Quadratic Residues
• Quadratic Reciprocity
• Pell’s Equation
• Fibonacci Numbers
• Linear Recurrence
• Gray Code
• Balanced Ternary

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Bit Manipulation

• Bit Operations
• Enumerating Submasks
• Enumerating Supermasks
• Subset DP
• SOS DP
• Bitset Optimization
• Builtin Bit Functions

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Data Structures

• Prefix Sum
• Difference Array
• Sqrt Decomposition (as a technique)
• DSU on Tree (as a technique)

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Dynamic Programming

• Introduction to Dynamic Programming
• Memoization
• Tabulation
• State Compression DP
• Bitmask DP
• Digit DP
• Tree DP
• Rerooting DP
• Interval DP
• Probability DP
• DP on DAG
• Profile DP
• Knapsack
• Longest Increasing Subsequence
• Longest Common Subsequence
• Edit Distance
• Divide and Conquer DP
• Convex Hull Trick (as a technique)
• Monotone Queue Optimization (as a technique)
• Alien Trick
• Slope Trick

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String Algorithms

• Prefix Function
• Z Function
• String Hashing
• Rolling Hash
• Polynomial Hashing
• Suffix Array (as a technique - construction algorithms are in Named)
• Suffix Automaton (as a concept)
• Suffix Tree (as a concept)

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Mathematics

• Matrix
• Determinant
• Rank
• Linear Basis (as a concept)
• XOR Basis (as a concept)

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Numerical Methods

• Binary Search
• Ternary Search
• Newton Method
• Golden Section Search
• Binary Search on Answer
• Coordinate Compression

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Geometry

• Geometry Basics
• Vectors
• Dot Product
• Cross Product
• Line Intersection
• Segment Intersection
• Circle Line Intersection
• Circle Circle Intersection
• Tangents
• Distance Between Points
• Orientation Test
• Convex Hull (as a concept)
• Minkowski Sum
• Rotating Calipers (as a technique)
• Point in Convex Polygon
• Polygon Area
• Pick’s Theorem
• Closest Pair of Points
• Half Plane Intersection
• Sweep Line (as a technique)
• Voronoi Diagram (concept)
• Delaunay Triangulation (concept)
• Minimum Enclosing Circle
• Manhattan Geometry

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Graph Theory

• Breadth First Search
• Depth First Search
• Topological Sort
• Connected Components
• Bridges
• Articulation Points
• Bridge Tree
• Strongly Connected Components (concept)
• Condensation Graph
• Biconnected Components
• SPFA
• 0‑1 BFS
• Dial Algorithm
• Lowest Common Ancestor (concept)
• Binary Lifting (technique)
• Euler Tour
• Heavy‑Light Decomposition (technique)
• Centroid Decomposition (technique)
• Virtual Tree (technique)
• Tree Isomorphism
• Tree Hashing
• Second Best MST
• Eulerian Path (concept)
• Hamiltonian Path (concept)
• Negative Cycle (detection)
• Minimum Cost Flow (concept)
• Circulation with Demands
• Bipartite Matching (concept)
• 2‑SAT
• Strong Orientation
• Dominator Tree (concept)
• Prüfer Code
• Euler Tour Tree (concept)
• Dynamic Connectivity (concept)

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Game Theory

• Combinatorial Games
• Nim
• Grundy Numbers (SG values)
• Minimax (as a concept)
• Alpha-Beta Pruning (as a concept)

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Scheduling

• Job Scheduling
• Interval Scheduling
• Greedy Scheduling
• Deadline Scheduling

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Polynomial / Algebra

• Polynomial Arithmetic
• Convolution (concept)
• FFT / NTT (concept)
• Formal Power Series

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Randomized / Approximation

• Randomized Algorithms (concept)
• Las Vegas vs Monte Carlo
• Approximation Algorithms (concept)

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Exact / NP‑Hard

• Backtracking
• Branch and Bound
• Meet‑in‑the‑Middle
• Exact Cover (concept)