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Concepts187

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📐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

All Beginner Intermediate Advanced

⚙️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.

#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

Aliens Trick (WQS Binary Search)

Aliens Trick (WQS Binary Search) converts a hard “exactly k items” optimization into an unconstrained problem by adding a penalty λ per chosen item.

#aliens trick#wqs binary search#parametric search+11

⚙️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

⚙️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

⚙️AlgorithmAdvanced

Convex Hull Trick - Dynamic (LineContainer)

Dynamic Convex Hull Trick (LineContainer) maintains the lower or upper envelope of lines y = m x + b with O(log n) insertion and O(log n) query for arbitrary insertion order.

#convex hull trick#dynamic cht#linecontainer+12

⚙️AlgorithmAdvanced

Convex Hull Trick (CHT)

The Convex Hull Trick (CHT) speeds up dynamic programs where each state is a minimum over linear functions, such as dp[i] = min_j (dp[j] + b[j] × a[i]).

#convex hull trick#cht#dynamic programming optimization+12

⚙️AlgorithmAdvanced

Knuth Optimization

Knuth Optimization speeds up a class of interval dynamic programming (DP) from O(n^3) to O(n^2) by exploiting the monotonicity of optimal split points.

#knuth optimization#interval dp#quadrangle inequality+12

⚙️AlgorithmAdvanced

Digit DP - Advanced States

Digit DP counts integers in a range by scanning digits from most significant to least while maintaining compact state information.

#digit dp#tight flag#leading zeros+12

⚙️AlgorithmAdvanced

DP with Probability

DP with probability models how chance flows between states over time by repeatedly redistributing mass according to transition probabilities.

#markov chain#probability dp#absorbing state+12