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Concepts80

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
⚙️AlgorithmAdvanced

Rectangle Union Area

The union area of many axis-aligned rectangles can be computed efficiently using a sweep line over x and a segment tree tracking covered y-length.

#rectangle union area#line sweep#segment tree+12
⚙️AlgorithmIntermediate

Basic Geometry - Lines and Segments

A line can be represented by two points, a point with a direction vector, or the general form ax + by + c = 0, and these forms are interconvertible.

#line intersection
12345
Advanced
Filtering by:
#competitive programming
#segment intersection
#orientation test
+12
⚙️AlgorithmAdvanced

Suffix Array Construction

A suffix array stores the starting indices of all suffixes of a string in lexicographic order, enabling fast substring queries and many string operations.

#suffix array#lcp array#kasai+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#booth algorithm#duval algorithm+12
⚙️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
⚙️AlgorithmAdvanced

Slope Trick

Slope Trick is a technique to maintain a convex piecewise-linear function implicitly using two heaps and a running constant.

#slope trick#convex dp#piecewise linear+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
⚙️AlgorithmAdvanced

Subset Sum Convolution

Subset Sum Convolution (often called Subset Convolution) computes C[S] by summing A[T]×B[U] over all disjoint pairs T and U whose union is S.

#subset convolution#subset sum convolution#sos dp+11
⚙️AlgorithmAdvanced

Divide and Conquer DP Optimization

Divide and Conquer DP optimization speeds up DP transitions of the form dp[i][j] = min over k of dp[i-1][k] + C(k, j) when the optimal k is monotone in j.

#divide and conquer dp#monge array#quadrangle inequality+10