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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

Knapsack Problems

Knapsack problems ask how to pick items under a weight (or cost) limit to maximize value or to check if a target sum is reachable.

#0/1 knapsack#unbounded knapsack#bounded knapsack+12
⚙️AlgorithmIntermediate

Coin Change and Variants

Coin Change uses dynamic programming to find either the minimum number of coins to reach a target or the number of ways to reach it.

#coin change
7891011
Advanced
#dynamic programming
#unbounded knapsack
+12
⚙️AlgorithmIntermediate

Dynamic Programming Fundamentals

Dynamic programming (DP) solves complex problems by breaking them into overlapping subproblems and using their optimal substructure.

#dynamic programming#memoization#tabulation+12
⚙️AlgorithmIntermediate

DP State Design

Dynamic Programming (DP) state design is the art of choosing what information to remember so that optimal substructure can be reused efficiently.

#dynamic programming#dp state#bitmask dp+11
⚙️AlgorithmIntermediate

Bipartite Matching - Hopcroft-Karp

Hopcroft–Karp computes maximum matching in a bipartite graph in O(E \sqrt{V}) time, which is asymptotically faster than repeated DFS (Kuhn's algorithm).

#hopcroft karp#bipartite matching#augmenting path+11
⚙️AlgorithmIntermediate

Bipartite Matching - Kuhn's Algorithm

Kuhn’s algorithm finds a maximum matching in a bipartite graph by repeatedly searching for augmenting paths using DFS.

#bipartite matching#kuhn algorithm#augmenting path+12
⚙️AlgorithmIntermediate

König's Theorem

König's Theorem states that in any bipartite graph, the size of a maximum matching equals the size of a minimum vertex cover.

#konig's theorem#bipartite matching#minimum vertex cover+12
⚙️AlgorithmIntermediate

Flow - Modeling Techniques

Many classic problems can be modeled as a maximum flow problem by building the right network and capacities.

#max flow#dinic#bipartite matching+12
⚙️AlgorithmIntermediate

Min-Cut Max-Flow Theorem

The Max-Flow Min-Cut Theorem says the maximum amount you can push from source to sink equals the minimum total capacity you must cut to disconnect them.

#max flow#min cut#edmonds karp+12
⚙️AlgorithmIntermediate

Maximum Flow - Dinic's Algorithm

Dinic's algorithm computes maximum flow by repeatedly building a level graph with BFS and sending a blocking flow using DFS.

#dinic#maximum flow#blocking flow+11
⚙️AlgorithmIntermediate

Maximum Flow - Ford-Fulkerson

Ford–Fulkerson finds the maximum possible flow from a source to a sink by repeatedly pushing flow along an augmenting path in the residual graph.

#maximum flow#ford-fulkerson#edmonds-karp+10
⚙️AlgorithmIntermediate

LCA - Binary Lifting

Binary lifting precomputes 2^k ancestors for every node so we can jump upward in powers of two.

#lca#binary lifting#tree+12