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Concepts52

Groups

📐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

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginner
⚙️AlgorithmAdvanced

Divide and Conquer DP Optimization

Divide and Conquer DP optimization speeds up DP transitions of the form dp[i][j] = min over k of dp[i-1][k] + C(k, j) when the optimal k is monotone in j.

#divide and conquer dp#monge array#quadrangle inequality+10
⚙️AlgorithmAdvanced

Convex Hull Trick - Dynamic (LineContainer)

Dynamic Convex Hull Trick (LineContainer) maintains the lower or upper envelope of lines y = m x + b with O(log n) insertion and O(log n) query for arbitrary insertion order.

12345
Intermediate
Advanced
Filtering by:
#competitive programming
#convex hull trick
#dynamic cht
#linecontainer
+12
⚙️AlgorithmAdvanced

Convex Hull Trick (CHT)

The Convex Hull Trick (CHT) speeds up dynamic programs where each state is a minimum over linear functions, such as dp[i] = min_j (dp[j] + b[j] × a[i]).

#convex hull trick#cht#dynamic programming optimization+12
⚙️AlgorithmAdvanced

Knuth Optimization

Knuth Optimization speeds up a class of interval dynamic programming (DP) from O(n^3) to O(n^2) by exploiting the monotonicity of optimal split points.

#knuth optimization#interval dp#quadrangle inequality+12
∑MathAdvanced

Berlekamp-Massey Algorithm

Berlekamp–Massey (BM) finds the shortest linear recurrence that exactly fits a given sequence over a field (e.g., modulo a prime).

#berlekamp-massey#linear recurrence#minimal polynomial+11
∑MathAdvanced

Gaussian Elimination over GF(2)

Gaussian elimination over GF(2) is ordinary Gaussian elimination where addition and subtraction are XOR and multiplication is AND.

#gaussian elimination#gf(2)#xor basis+12
⚙️AlgorithmAdvanced

General Matching - Blossom Algorithm

Edmonds' Blossom Algorithm finds a maximum matching in any undirected graph, not just bipartite ones.

#blossom algorithm#edmonds matching#general graph matching+12
⚙️AlgorithmAdvanced

Biconnected Components

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

#biconnected components#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

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

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