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Concepts356

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

Greedy - Exchange Argument

The exchange argument proves a greedy algorithm is optimal by swapping out-of-order choices in any supposed optimal solution until it matches the greedy one without making it worse.

#greedy#exchange argument#pairwise swap+12
⚙️AlgorithmIntermediate

Greedy Algorithms

Greedy algorithms build a solution step by step by always taking the best local choice available.

#greedy algorithms
2627282930
Advanced
#activity selection
#interval scheduling
+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
⚙️AlgorithmIntermediate

Ternary Search

Ternary search finds the maximum or minimum of a unimodal function on a line by probing two interior points and discarding one third of the interval each step.

#ternary search#unimodal function#convex optimization+12
⚙️AlgorithmIntermediate

Binary Search on Answer

Binary Search on Answer turns an optimization problem into a yes/no decision problem over a monotonic answer space.

#binary search on answer#parametric search#monotonic predicate+12
⚙️AlgorithmIntermediate

Two Pointers

Two pointers is a pattern where two indices move through a sequence in a coordinated, usually monotonic way to avoid unnecessary work.

#two pointers#sliding window#opposite ends+12
⚙️AlgorithmIntermediate

Binary Search

Binary search quickly finds targets or boundaries in sorted or monotonic data by halving the search interval each step.

#binary search#lower_bound#upper_bound+11
🗂️Data StructureIntermediate

Merge Sort Tree

A Merge Sort Tree is a segment tree where every node stores the sorted list of values in its segment.

#merge sort tree#segment tree#range query+12
🗂️Data StructureIntermediate

Sqrt Decomposition

Sqrt decomposition partitions an array into about \(\sqrt{n}\) blocks, each of size about \(\sqrt{n}\), to speed up range queries and updates.

#sqrt decomposition#block decomposition#bucket decomposition+11
🗂️Data StructureIntermediate

Iterative Segment Tree

An iterative segment tree stores all leaves in tree[n..2n-1] and internal nodes in tree[1..n-1], enabling O(\log n) point updates and range queries without recursion.

#iterative segment tree#segment tree#non-recursive+12
🗂️Data StructureIntermediate

Binary Trie for XOR

A binary trie (also called a bitwise trie) stores numbers by their binary bits, branching on 0/1 at each level.

#binary trie#bitwise trie#xor+12
🗂️Data StructureIntermediate

Segment Tree with Lazy Propagation

A segment tree with lazy propagation supports fast range updates and range queries in O(\log n) time.

#segment tree#lazy propagation#range update+12