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Concepts532

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

AllBeginnerIntermediateAdvanced
∑MathIntermediate

Prime Factorization

Prime factorization expresses any integer greater than 1 as a product of primes raised to powers, uniquely up to ordering.

#prime factorization#trial division#spf sieve+12
∑MathIntermediate

Extended Euclidean Algorithm

The Extended Euclidean Algorithm finds integers x and y such that ax + by = gcd(a, b) while also computing gcd(a, b).

#extended euclidean algorithm
2930313233
#bezout coefficients
#gcd
+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
∑MathIntermediate

Sieve of Eratosthenes

The Sieve of Eratosthenes marks multiples of each prime to find all primes up to n in O(n log log n) time.

#sieve of eratosthenes#segmented sieve#linear sieve+11
∑MathIntermediate

GCD and Euclidean Algorithm

The greatest common divisor (gcd) of two integers is the largest integer that divides both without a remainder.

#gcd#euclidean algorithm#extended euclidean+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
⚙️AlgorithmIntermediate

Randomized Algorithms

Randomized algorithms use coin flips (random bits) to guide choices, often making code simpler and fast on average.

#randomized algorithms#las vegas#monte carlo+12
⚙️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
⚙️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