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Concepts141

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

Convex Hull

The convex hull is the smallest convex polygon that contains all given points, like a rubber band snapped around nails on a board.

#convex hull#graham scan#monotone chain+12
⚙️AlgorithmIntermediate

Minimum Rotation

The minimum rotation of a string is the lexicographically smallest string you can get by cutting it at some position and swapping the two parts.

#minimum rotation
56789
Advanced
#booth algorithm
#duval algorithm
+12
⚙️AlgorithmIntermediate

Point in Polygon

Point-in-polygon decides whether a point lies outside, inside, or on the boundary of a polygon.

#point in polygon#ray casting#winding number+11
⚙️AlgorithmIntermediate

Orientation and CCW

Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.

#orientation#ccw#cross product+12
⚙️AlgorithmIntermediate

Basic Geometry - Points and Vectors

A 2D point can be treated as a vector from the origin, so vector math (addition, scaling, dot, cross) applies directly to points.

#geometry#vector#dot product+11
⚙️AlgorithmIntermediate

KMP - Prefix Function Applications

The prefix function π of a string tells, for every position, the length of the longest proper prefix that is also a suffix of the prefix ending there.

#kmp#prefix function#failure function+11
⚙️AlgorithmIntermediate

Z-Function

The Z-function of a string S computes for each position i the length of the longest substring starting at i that matches the prefix of S.

#z-function#z algorithm#string matching+12
⚙️AlgorithmIntermediate

KMP Algorithm

The KMP algorithm finds all occurrences of a pattern in a text in O(n + m) time by never re-checking characters that are already known to match or mismatch.

#kmp algorithm#prefix function#failure function+12
⚙️AlgorithmIntermediate

Manacher's Algorithm

Manacher's algorithm finds the length of the longest palindrome centered at every position in a string in linear time O(n).

#manacher's algorithm#palindromic substring#longest palindromic substring+11
⚙️AlgorithmIntermediate

String Hashing (Polynomial Hash)

Polynomial string hashing encodes a string as a base-p number modulo a large prime, letting us compare substrings in O(1) after O(n) preprocessing.

#string hashing#polynomial hash#rolling hash+12
⚙️AlgorithmIntermediate

Exchange Arguments in DP

An exchange argument proves that any optimal solution can be reordered to satisfy a simple sorting rule by showing that swapping adjacent out-of-order elements never helps.

#exchange argument#adjacent swap#smith rule+12
⚙️AlgorithmIntermediate

Interval DP

Interval DP solves problems where the optimal answer for a segment [i, j] depends on answers of its subsegments.

#interval dp#matrix chain multiplication#burst balloons+12