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Concepts80

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

Tree Isomorphism

Tree isomorphism asks whether two trees have exactly the same shape, ignoring vertex names.

#tree isomorphism#ahu algorithm#canonical form+12
⚙️AlgorithmAdvanced

DP on Broken Profile - Plug DP

Plug DP (DP on broken profile with plugs) sweeps a grid cell by cell while remembering how partial path segments cross the frontier as labeled “plugs.”

#plug dp
12345
Advanced
Filtering by:
#competitive programming
#broken profile
#hamiltonian path
+12
⚙️AlgorithmAdvanced

Matrix Exponentiation - Advanced

Matrix exponentiation turns repeated linear transitions into fast O(n^{3} log k) computation using exponentiation by squaring.

#matrix exponentiation#adjacency matrix#walk counting+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#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

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
⚙️AlgorithmIntermediate

Matrix Exponentiation

Matrix exponentiation turns repeated linear transitions into a single fast power of a matrix using exponentiation by squaring.

#matrix exponentiation#binary exponentiation#companion matrix+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

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
⚙️AlgorithmIntermediate

Small-to-Large Merging

Small-to-large merging is a technique where you always merge the smaller container into the larger one to guarantee low total work.

#small-to-large merging#dsu on tree#sack technique+11
⚙️AlgorithmIntermediate

Mo's Algorithm

Mo's algorithm answers many range queries offline by reordering them to minimize pointer movement along the array.

#mo's algorithm#offline queries#range queries+12