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Concepts46

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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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AllBeginnerIntermediate
⚙️AlgorithmAdvanced

Voronoi Diagram and Delaunay

Voronoi diagrams partition the plane so each region contains points closest to one site, while the Delaunay triangulation connects sites whose Voronoi cells touch.

#voronoi diagram#delaunay triangulation#fortune algorithm+12
⚙️AlgorithmAdvanced

Sqrt Decomposition on Queries

Sqrt decomposition on queries (time blocking) processes Q operations in blocks of size about \(\sqrt{Q}\) to balance per-query overhead and rebuild cost.

#sqrt decomposition
1234
Advanced
#time blocking
#query blocking
+12
⚙️AlgorithmAdvanced

Polynomial Operations

Fast polynomial operations treat coefficients like numbers but use FFT/NTT to multiply in O(n \log n) time instead of O(n^2).

#polynomial#ntt#fft+12
⚙️AlgorithmAdvanced

Parallel Binary Search

Parallel Binary Search (PBS) lets you binary-search the answers of many queries at once by batching them by their current mid value.

#parallel binary search#offline queries#monotone predicate+10
⚙️AlgorithmAdvanced

Convolution Applications

Convolution turns local pairwise combinations (like matching characters or adding two dice) into a single fast transform–multiply–inverse pipeline.

#convolution#fft#ntt+12
⚙️AlgorithmAdvanced

NTT (Number Theoretic Transform)

The Number Theoretic Transform (NTT) is an FFT-like algorithm that performs discrete convolutions exactly using modular arithmetic instead of floating-point numbers.

#ntt#number theoretic transform#polynomial multiplication+11
⚙️AlgorithmAdvanced

FFT (Fast Fourier Transform)

FFT converts a polynomial from coefficients to values at the n-th roots of unity in O(n log n) time, enabling fast multiplication via pointwise products.

#fft#polynomial multiplication#convolution+11
⚙️AlgorithmAdvanced

CDQ Divide and Conquer

CDQ divide and conquer is an offline technique that splits the timeline (or one coordinate) and lets updates from the left half contribute to queries in the right half.

#cdq divide and conquer#offline algorithm#fenwick tree+11
⚙️AlgorithmAdvanced

Mo's Algorithm - With Updates

Mo's algorithm with updates treats array modifications as a third dimension called time and answers range queries on the correct version of the array.

#mo's algorithm with updates#time dimension#offline range queries+11
⚙️AlgorithmAdvanced

Half-Plane Intersection

Half-plane intersection (HPI) computes the common region that satisfies many linear side-of-line constraints in the plane.

#half-plane intersection#computational geometry#convex polygon+12
⚙️AlgorithmAdvanced

Minkowski Sum

The Minkowski sum A ⊕ B adds every point of set A to every point of set B, and for convex polygons it can be computed in O(n + m) by merging edge directions.

#minkowski sum#convex polygon#edge merge+12
⚙️AlgorithmAdvanced

DSU on Tree (Sack)

DSU on Tree (also called the Sack technique) answers many subtree queries in O(n \log n) by keeping data from the heavy child and temporarily re-adding light subtrees.

#dsu on tree#sack technique#subtree queries+12