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Concepts172

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📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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⚙️AlgorithmAdvanced

Minimum Cost Maximum Flow

Minimum Cost Maximum Flow (MCMF) finds the maximum possible flow from a source to a sink while minimizing the total cost paid per unit of flow along edges.

#minimum cost maximum flow#successive shortest augmenting path#reduced cost+11
⚙️AlgorithmAdvanced

Biconnected Components

A biconnected component (block) is a maximal subgraph where removing any single vertex keeps it connected.

#biconnected components
1112131415
Advanced
#blocks
#articulation points
+12
⚙️AlgorithmAdvanced

Virtual Tree (Auxiliary Tree)

A Virtual Tree (Auxiliary Tree) compresses a large tree into a much smaller tree that contains only the k important nodes and the LCAs needed to keep them connected.

#virtual tree#auxiliary tree#lca+12
⚙️AlgorithmAdvanced

Johnson's Algorithm

Johnson's Algorithm computes all-pairs shortest paths on sparse graphs by first removing negative edges via reweighting, then running Dijkstra from every vertex.

#johnson's algorithm#all pairs shortest paths#apsp+12
🗂️Data StructureAdvanced

Kinetic Tournament Tree

A kinetic tournament tree maintains the minimum (or maximum) of moving values whose pairwise order can change over time.

#kinetic data structure#tournament tree#certificate+12
🗂️Data StructureAdvanced

Aho-Corasick - DP Applications

Aho–Corasick (AC) turns a set of forbidden patterns into a finite automaton that lets you process or generate strings while tracking whether any pattern appears.

#aho-corasick#automaton dp#forbidden substrings+12
🗂️Data StructureAdvanced

Li Chao Tree

A Li Chao tree maintains a set of lines y = m x + b and answers minimum (or maximum) value queries at a given x in O(log C) time, where C is the numeric range of x.

#li chao tree#dynamic convex hull#segment tree lines+12
🗂️Data StructureAdvanced

Palindromic Tree (Eertree)

A Palindromic Tree (Eertree) stores every distinct palindromic substring of a string as a node and can be built online in linear time.

#palindromic tree#eertree#palindromic substrings+12
🗂️Data StructureAdvanced

Suffix Automaton - Advanced Usage

A suffix automaton (SAM) is a compact DFA that captures all distinct substrings of a string and supports many advanced queries in linear time.

#suffix automaton#endpos#suffix link+12
🗂️Data StructureAdvanced

Suffix Automaton

A suffix automaton (SAM) is the minimal deterministic finite automaton that recognizes all substrings of a string, built online in O(n) time and space.

#suffix automaton#endpos equivalence#suffix link+12
🗂️Data StructureAdvanced

Aho-Corasick Automaton

Aho–Corasick is a trie with failure links that finds all occurrences of many patterns in a single pass over the text.

#aho-corasick#multi-pattern matching#trie+12
🗂️Data StructureAdvanced

Suffix Array - LCP Array Applications

The LCP (Longest Common Prefix) array, built alongside a suffix array, unlocks fast solutions to problems like longest repeated substring, number of distinct substrings, and longest common substring.

#suffix array#lcp array#kasai algorithm+12