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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

AllBeginnerIntermediateAdvanced
⚙️AlgorithmAdvanced

Sum over Subsets (SOS) DP

Sum over Subsets (SOS) DP lets you compute F[mask] = sum of A[submask] over all submasks in O(n 2^n) instead of O(3^n).

#sos dp#subset zeta transform#mobius inversion+11
⚙️AlgorithmAdvanced

DP with Expected Value

Dynamic programming with expected value solves problems where each state transitions randomly and we seek the expected cost, time, or steps to reach a goal.

#expected value dp
910111213
#linearity of expectation
#indicator variables
+11
⚙️AlgorithmIntermediate

Interval DP

Interval DP solves problems where the optimal answer for a segment [i, j] depends on answers of its subsegments.

#interval dp#matrix chain multiplication#burst balloons+12
⚙️AlgorithmIntermediate

Tree DP - Rerooting Technique

Rerooting (a.k.a. 换根 DP) computes a per-node answer as if each node were the root, in total O(n) time on trees.

#rerooting#tree dp#prefix suffix+11
⚙️AlgorithmIntermediate

Digit DP

Digit DP is a dynamic programming technique for counting or aggregating values over all integers in a range that satisfy a digit-based property.

#digit dp#dynamic programming#tight constraint+12
⚙️AlgorithmIntermediate

LIS Variants

LIS variants extend the classic longest increasing subsequence to handle non-decreasing sequences, counting how many LIS exist, and maximizing the sum of a subsequence.

#lis#lnds#patience sorting+12
⚙️AlgorithmIntermediate

Tree DP - Matching and Covering

Tree DP solves matching, vertex cover, and independent set on trees in linear time using small state transitions per node.

#tree dp#maximum matching#vertex cover+12
⚙️AlgorithmIntermediate

Bitmask DP

Bitmask DP compresses the state of a subset of n elements into an integer mask, enabling elegant dynamic programming over all subsets.

#bitmask dp#subset dp#held-karp+12
⚙️AlgorithmIntermediate

Longest Common Subsequence

The Longest Common Subsequence (LCS) between two sequences is the longest sequence that appears in both, not necessarily contiguously.

#longest common subsequence#lcs#string dp+12
⚙️AlgorithmIntermediate

Bitmask DP - Subset Enumeration

Bitmask DP subset enumeration lets you iterate all submasks of a given mask using the idiom for (s = mask; s > 0; s = (s - 1) & mask).

#bitmask#submask enumeration#superset enumeration+11
⚙️AlgorithmIntermediate

DP on Trees

DP on trees is a technique that computes answers for each node by combining results from its children using a post-order DFS.

#tree dp#post-order dfs#rerooting+12
⚙️AlgorithmIntermediate

Edit Distance

Edit distance (Levenshtein distance) measures the minimum number of inserts, deletes, and replaces needed to turn one string into another.

#edit distance#levenshtein#dynamic programming+11