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Concepts356

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

State Space Reduction

State space reduction shrinks the number of dynamic programming or search states by keeping only the information that truly affects future decisions.

#state space reduction#dynamic programming#equivalence relation+12
⚙️AlgorithmIntermediate

Fix One Variable Technique

The Fix One Variable technique reduces multi-variable search problems by enumerating one variable explicitly and optimizing over the others with structure.

#fix one variable
1314151617
Advanced
#dimension reduction
#two pointers
+12
⚙️AlgorithmIntermediate

Offline Query Processing

Offline query processing means you collect all queries first and answer them later in a smart order that makes updates/queries cheap.

#offline query processing#mo's algorithm#fenwick tree+12
⚙️AlgorithmIntermediate

Invariant Maintenance

An invariant is a property you promise to keep true throughout an algorithm, and it is the anchor of both design and correctness proofs.

#invariant#loop invariant#search invariant+12
⚙️AlgorithmIntermediate

Hill Climbing and Local Search

Hill climbing is an iterative optimization method that repeatedly moves to a better neighboring solution until no improvement is possible, reaching a local optimum.

#hill climbing#local search#steepest ascent+12
⚙️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#metropolis criterion#acceptance probability+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
⚙️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