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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
⚙️AlgorithmIntermediate

Circle Geometry

Circle geometry in computational geometry relies on precise vector math, quadratic equations, and careful floating-point handling with an EPS tolerance.

#circle geometry#line circle intersection#circle circle intersection+12
⚙️AlgorithmIntermediate

Simulated Annealing

Simulated annealing is a probabilistic search that sometimes accepts worse moves to escape local optima, mimicking how metals cool and crystallize.

#simulated annealing
1920212223
#metropolis criterion
#acceptance probability
+12
🗂️Data StructureAdvanced

Persistent DSU (Fully Persistent Union-Find)

A persistent DSU (Union-Find) keeps all historical versions so you can query connectivity at any past version and even branch new futures from old states.

#persistent dsu#fully persistent union-find#union by rank+12
⚙️AlgorithmIntermediate

Bitset Optimization

Bitset optimization exploits word-level parallelism so one CPU instruction processes 64 bits at once on typical 64-bit machines.

#bitset#word-level parallelism#bitmask+12
⚙️AlgorithmIntermediate

Bidirectional BFS (Meet in the Middle Search)

Bidirectional BFS searches forward from the start and backward from the goal to meet in the middle, drastically reducing explored states.

#bidirectional bfs#meet in the middle#two-ended search+11
⚙️AlgorithmIntermediate

XOR Hashing (Zobrist Hashing)

XOR (Zobrist) hashing assigns a random 64-bit number to each possible element and hashes a set by XORing the numbers of present elements.

#xor hashing#zobrist hashing#incremental hashing+11
⚙️AlgorithmAdvanced

Directed MST (Edmonds/Chu-Liu Algorithm)

A directed minimum spanning arborescence (MSA) is a minimum-cost set of edges that makes every vertex reachable from a chosen root with exactly one incoming edge per non-root vertex.

#directed mst#edmonds algorithm#chu-liu+11
∑MathAdvanced

Floor Sum Formula

The floor sum computes S(n,m,a,b) = sum_{i=0}^{n-1} floor((a i + b)/m) efficiently in O(log(min(a,m))) time.

#floor sum#atcoder library#euclidean algorithm+12
⚙️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
⚙️AlgorithmIntermediate

Tree Isomorphism

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

#tree isomorphism#ahu algorithm#canonical form+12
∑MathIntermediate

Legendre's Formula

Legendre's formula gives the exponent of a prime p in n! by summing how many multiples of p, p^2, p^3, ... are ≤ n.

#legendre's formula#p-adic valuation#binomial divisibility+10
∑MathIntermediate

Harmonic Lemma

The Harmonic Lemma says that the values of \lfloor n/i \rfloor only change about 2\sqrt{n} times, so you can iterate those value blocks in O(\sqrt{n}) instead of O(n).

#harmonic lemma#integer division trick#block decomposition+12