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Concepts9

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

AllBeginnerIntermediate
⚙️AlgorithmIntermediate

Functional Graph

A functional graph is a directed graph where every node has exactly one outgoing edge, so repeatedly following edges from any start eventually loops into a cycle.

#functional graph#successor graph#cycle detection+10
⚙️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
Advanced
Filtering by:
#binary lifting
#biconnected components
#articulation points
+11
⚙️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
⚙️AlgorithmIntermediate

LCA - Binary Lifting

Binary lifting precomputes 2^k ancestors for every node so we can jump upward in powers of two.

#lca#binary lifting#tree+12
⚙️AlgorithmIntermediate

Bridge Tree

A bridge tree is built by contracting every 2-edge-connected component of an undirected graph into a single node, leaving only bridges as edges between nodes.

#bridge tree#2-edge-connected components#bridges+12
⚙️AlgorithmIntermediate

Tree Distances and Diameter

Tree diameter is the longest simple path in a tree and can be found with two BFS/DFS runs.

#tree diameter#tree center#eccentricity+12
⚙️AlgorithmIntermediate

Lowest Common Ancestor (LCA)

The Lowest Common Ancestor (LCA) of two nodes in a rooted tree is the deepest node that is an ancestor of both.

#lowest common ancestor#binary lifting#euler tour+12
⚙️AlgorithmIntermediate

Minimum Spanning Tree - Kruskal

Kruskal’s algorithm builds a minimum spanning tree (MST) by sorting all edges by weight and greedily picking the next lightest edge that does not form a cycle.

#kruskal#minimum spanning tree#mst+11
🗂️Data StructureAdvanced

Centroid Decomposition

Centroid decomposition splits a tree around a special node (centroid) so that every remaining component has at most half the nodes.

#centroid decomposition#centroid tree#tree algorithms+11