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How I Study AI - Learn AI Papers & Lectures the Easy Way

Concepts532

Groups

๐Ÿ“Linear Algebra15๐Ÿ“ˆCalculus & Differentiation10๐ŸŽฏOptimization14๐ŸŽฒProbability Theory12๐Ÿ“ŠStatistics for ML9๐Ÿ“กInformation Theory10๐Ÿ”บConvex Optimization7๐Ÿ”ขNumerical Methods6๐Ÿ•ธGraph Theory for Deep Learning6๐Ÿ”ตTopology for ML5๐ŸŒDifferential Geometry6โˆžMeasure Theory & Functional Analysis6๐ŸŽฐRandom Matrix Theory5๐ŸŒŠFourier Analysis & Signal Processing9๐ŸŽฐSampling & Monte Carlo Methods10๐Ÿง Deep Learning Theory12๐Ÿ›ก๏ธRegularization Theory11๐Ÿ‘๏ธAttention & Transformer Theory10๐ŸŽจGenerative Model Theory11๐Ÿ”ฎRepresentation Learning10๐ŸŽฎReinforcement Learning Mathematics9๐Ÿ”„Variational Methods8๐Ÿ“‰Loss Functions & Objectives10โฑ๏ธSequence & Temporal Models8๐Ÿ’ŽGeometric Deep Learning8

Category

๐Ÿ”ทAllโˆ‘Mathโš™๏ธAlgo๐Ÿ—‚๏ธDS๐Ÿ“šTheory

Level

AllBeginnerIntermediateAdvanced
โš™๏ธAlgorithmIntermediate

KMP Algorithm

The KMP algorithm finds all occurrences of a pattern in a text in O(n + m) time by never re-checking characters that are already known to match or mismatch.

#kmp algorithm#prefix function#failure function+12
โš™๏ธ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
3233343536
#palindromic substring
#longest palindromic substring
+11
โš™๏ธAlgorithmAdvanced

Slope Trick

Slope Trick is a technique to maintain a convex piecewise-linear function implicitly using two heaps and a running constant.

#slope trick#convex dp#piecewise linear+11
โš™๏ธ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
โš™๏ธAlgorithmAdvanced

Aliens Trick (WQS Binary Search)

Aliens Trick (WQS Binary Search) converts a hard โ€œexactly k itemsโ€ optimization into an unconstrained problem by adding a penalty ฮป per chosen item.

#aliens trick#wqs binary search#parametric search+11
โš™๏ธ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
โš™๏ธAlgorithmAdvanced

Subset Sum Convolution

Subset Sum Convolution (often called Subset Convolution) computes C[S] by summing A[T]ร—B[U] over all disjoint pairs T and U whose union is S.

#subset convolution#subset sum convolution#sos dp+11
โš™๏ธ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
โš™๏ธ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
โš™๏ธ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] ร— a[i]).

#convex hull trick#cht#dynamic programming optimization+12
โš™๏ธ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
โš™๏ธ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