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Concepts46

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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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AllBeginnerIntermediate
⚙️AlgorithmAdvanced

DP with Probability

DP with probability models how chance flows between states over time by repeatedly redistributing mass according to transition probabilities.

#markov chain#probability dp#absorbing state+12
⚙️AlgorithmAdvanced

Sum over Subsets (SOS) DP

Sum over Subsets (SOS) DP lets you compute F[mask] = sum of A[submask] over all submasks in O(n 2^n) instead of O(3^n).

#sos dp
1234
Advanced
#subset zeta transform
#mobius inversion
+11
⚙️AlgorithmAdvanced

DP with Expected Value

Dynamic programming with expected value solves problems where each state transitions randomly and we seek the expected cost, time, or steps to reach a goal.

#expected value dp#linearity of expectation#indicator variables+11
⚙️AlgorithmAdvanced

Block-Cut Tree

A Block-Cut Tree decomposes an undirected graph into biconnected components (blocks) and articulation points, forming a bipartite tree.

#block-cut tree#biconnected components#articulation points+11
⚙️AlgorithmAdvanced

Hungarian Algorithm

The Hungarian algorithm solves the square assignment problem (matching n workers to n jobs) in O(n^{3}) time using a clever potential (label) function on vertices.

#hungarian algorithm#assignment problem#bipartite matching+11
⚙️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

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#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