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Concepts13

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

Complexity Analysis Quick Reference

Use an operation budget of about 10^8 simple operations per second on typical online judges; always multiply by the time limit and number of test files if known.

#time complexity#competitive programming#big-o+12
⚙️AlgorithmIntermediate

Small-to-Large Principle

Small-to-large means always merge the smaller container into the larger one to keep total work low.

#small-to-large
12
Advanced
Filtering by:
#amortized analysis
#sack technique
#dsu on tree
+11
⚙️AlgorithmIntermediate

Double Counting

Double counting is the strategy of counting the same quantity in two different ways to derive an equality or an efficient algorithm.

#double counting#contribution technique#handshake lemma+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

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
📚TheoryIntermediate

Amortized Analysis

Amortized analysis measures the average cost per operation over a worst-case sequence, not over random inputs.

#amortized analysis#aggregate method#accounting method+12
⚙️AlgorithmIntermediate

Small-to-Large Merging

Small-to-large merging is a technique where you always merge the smaller container into the larger one to guarantee low total work.

#small-to-large merging#dsu on tree#sack technique+11
⚙️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

Sliding Window

Sliding window is a technique that moves a contiguous segment (window) across an array or string while maintaining some running information like sum, count, or max.

#sliding window#two pointers#variable window+11
🗂️Data StructureIntermediate

Disjoint Set Union (Union-Find)

Disjoint Set Union (Union-Find) maintains a collection of non-overlapping sets and supports fast merging and membership queries.

#disjoint set union#union-find#path compression+11
🗂️Data StructureIntermediate

Queue and Deque

A queue is a First-In-First-Out (FIFO) line where you add at the back and remove from the front in O(1) time.

#queue#deque#fifo+12
🗂️Data StructureIntermediate

Monotonic Deque

A monotonic deque is a double-ended queue that keeps elements in increasing or decreasing order so that the front always holds the current optimum (min or max).

#monotonic deque#sliding window maximum#sliding window minimum+12