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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

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🔷All∑Math⚙️Algo🗂️DS📚Theory

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🗂️Data StructureAdvanced

Dominator Tree

A dominator tree summarizes “must-pass” relationships in a directed graph from a chosen root r: u dominates v if every path from r to v goes through u.

#dominator tree#lengauer tarjan#semidominator+10
🗂️Data StructureAdvanced

Chtholly Tree (ODT - Old Driver Tree)

Chtholly Tree (ODT) stores an array as a set of non-overlapping value-constant intervals and updates by cutting and replacing whole ranges.

#odt
1819202122
#chtholly tree
#range assign
+9
⚙️AlgorithmIntermediate

Contribution Technique

The contribution technique flips perspective: compute how much each element contributes to the total, then sum these contributions.

#contribution technique#monotonic stack#sum of subarray minimums+12
⚙️AlgorithmIntermediate

Think Backwards (Reverse Thinking)

Think Backwards is a problem‑solving pattern where you reverse time or direction so hard deletions become easy insertions and the final state becomes the starting point.

#think backwards#reverse thinking#offline queries+12
⚙️AlgorithmIntermediate

Sweepline Technique

The sweep line technique processes geometric or time-based events in sorted order and maintains an active set that reflects the current state at the sweep position.

#sweep line#plane sweep#active set+12
⚙️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#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
⚙️AlgorithmAdvanced

3D Geometry Basics

3D geometry relies on a small toolkit: vectors, dot products, cross products, and planes; mastering these unlocks most 3D problem-solving.

#3d geometry#dot product#cross product+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
🗂️Data StructureAdvanced

Segment Tree with Range Affine Transformation

A segment tree with lazy propagation can support range updates of the form x → a·x + b (affine transformations) and range-sum queries in O(log n) per operation.

#segment tree#lazy propagation#affine update+12