legacy collection

Classical algorithms and heuristics.

The original 205 algonow lessons pair an algorithm with the heuristic that guides it. Explore the live diagrams, tested Python solutions, and complete narrations.

New puzzles focus on Python AI architecture and engineering. This collection remains available at its original lesson URLs.

Browse all 205 lessons AI engineering puzzles

settledfrontierpatha* × manhattan, live

all 205 legacy lessons

Sorting & Selection

puzzle 10▶ ~8 min

Quicksort×Median-of-three pivot

In-place comparison sorting

puzzle 33▶ ~8 min

Timsort×Galloping merge threshold

Real-world stable sorting

puzzle 107▶ ~8 min

LSD radix sort×Stable digit-bucket passes

Fixed-width key sorting

Data Structures

puzzle 08▶ ~8 min

Union-find×Union by rank with path compression

Components that only merge

puzzle 22▶ ~8 min

Binary search×Halving invariant

Sorted-array lookup

puzzle 26▶ ~8 min

Fenwick tree×Low-bit ladders

Prefix sums under change

puzzle 30▶ ~8 min

Skip list×Coin-flip level promotion

Ordered maps by lottery

puzzle 35▶ ~8 min

B-tree×High-fanout node splits

Disk-friendly ordered index

puzzle 51▶ ~8 min

Trie×Shared-prefix branching

Prefix-keyed dictionary

puzzle 53▶ ~8 min

Interval tree×Max-endpoint subtree pruning

Stabbing queries

puzzle 58▶ ~8 min

Ternary search×Two-probe interval thirds

Unimodal maximum finding

puzzle 62▶ ~8 min

Mo's algorithm×Sqrt block query ordering

Offline range queries

puzzle 71▶ ~8 min

B+ tree×Linked-leaf range scans

Database range index

puzzle 106▶ ~8 min

Treap×Random heap priorities

Ordered dictionaries, randomized

puzzle 139▶ ~8 min

Cuckoo hashing×Two-table eviction kicks

Worst-case-constant lookup

puzzle 163▶ ~10 min

Fibonacci heap×Lazy consolidation with marking

Amortized-optimal priority queue

puzzle 165▶ ~10 min

AVL tree×Height-balance rotations

Strictly balanced dictionary

Graph Algorithms

puzzle 01▶ ~7 min

A* search×Manhattan distance

Shortest paths on grid maps

puzzle 07▶ ~8 min

Dijkstra's algorithm×Binary heap priority queue

Nonnegative shortest paths

puzzle 15▶ ~8 min

Dinic's algorithm×Level-graph blocking flows

Maximum flow through a network

puzzle 21▶ ~8 min

Kahn's algorithm×Zero in-degree queue

Ordering dependencies

puzzle 23▶ ~8 min

Kruskal's algorithm×Union-find cycle test

Minimum spanning trees

puzzle 34▶ ~8 min

Bellman-Ford×Early-exit relaxation

Negative-edge shortest paths

puzzle 43▶ ~8 min

Hopcroft-Karp×Layered augmenting phases

Bipartite maximum matching

puzzle 50▶ ~8 min

Floyd-Warshall×Intermediate-vertex sweep

All-pairs shortest paths

puzzle 52▶ ~8 min

Tarjan's SCC algorithm×Low-link stack discipline

Strongly connected components

puzzle 57▶ ~8 min

Edmonds-Karp×Shortest augmenting paths

Maximum flow

puzzle 69▶ ~8 min

Push-relabel×FIFO vertex selection

Maximum flow

puzzle 72▶ ~8 min

Hungarian algorithm×Tight-edge alternating paths

Optimal assignment

puzzle 77▶ ~8 min

Prim's algorithm×Cheapest crossing edge

Minimum spanning trees

puzzle 82▶ ~8 min

Karger's algorithm×Random edge contraction

Minimum cut

puzzle 98▶ ~8 min

Louvain method×Greedy modularity moves

Community detection

puzzle 102▶ ~8 min

Johnson's algorithm×Reweighting potentials

Sparse all-pairs shortest paths

puzzle 122▶ ~8 min

Contraction hierarchies×Node-importance contraction order

Continental road routing

puzzle 123▶ ~8 min

Bron-Kerbosch×Tomita pivoting

Maximal clique listing

puzzle 142▶ ~8 min

Betweenness centrality×Brandes accumulation

Node importance

puzzle 155▶ ~9 min

IDA*×Manhattan distance

Memory-bound puzzle search

puzzle 168▶ ~10 min

Greedy graph coloring×DSatur saturation ordering

Vertex coloring

puzzle 198▶ ~10 min

Fruchterman-Reingold×Force-directed placement

Graph layout

Dynamic Programming & Combinatorics

puzzle 13▶ ~8 min

Kadane's algorithm×Running maximum

The brightest stretch of an array

puzzle 74▶ ~8 min

Longest increasing subsequence×Patience piles with binary search

Longest increasing subsequence

puzzle 81▶ ~8 min

Held-Karp×Bitmask subset states

Exact traveling salesman

puzzle 180▶ ~10 min

Gray code generation×Reflected binary

Subset enumeration

puzzle 206▶ ~10 min

Lexicographic permutations×Next-permutation algorithm

Permutation generation

Optimization & Operations Research

puzzle 02▶ ~7 min

Simulated annealing×Geometric cooling schedule

Traveling-salesman tours

puzzle 17▶ ~8 min

LRU caching×Least-recently-used eviction

Page and cache replacement

puzzle 39▶ ~8 min

Activity selection×Earliest-finish-first greedy

Non-overlapping selection

puzzle 48▶ ~8 min

Earliest deadline first×Dynamic deadline priority

Real-time scheduling

puzzle 67▶ ~8 min

Rate-monotonic scheduling×Shorter period wins

Real-time task scheduling

puzzle 73▶ ~8 min

Gale-Shapley×Deferred acceptance

Stable matching

puzzle 89▶ ~8 min

Greedy set cover×Maximum-coverage selection

Set cover approximation

puzzle 108▶ ~8 min

Secretary problem×1/e stopping rule

Optimal stopping

puzzle 117▶ ~8 min

Christofides×Matching plus Euler tour

Metric TSP approximation

puzzle 131▶ ~8 min

First fit decreasing×Descending size order

Bin packing

puzzle 135▶ ~8 min

Binomial options pricing×Cox-Ross-Rubinstein lattice

Option pricing

puzzle 170▶ ~10 min

Black-Scholes×Closed-form European pricing

Option pricing

puzzle 178▶ ~10 min

Round-robin scheduling×Time quantum

CPU scheduling

puzzle 185▶ ~10 min

Matrix exponentiation×Binary exponentiation

Linear recurrence evaluation

puzzle 186▶ ~12 min

Ski rental×Break-even deterministic rule

Rent-or-buy decisions

puzzle 188▶ ~10 min

Vickrey auction×Second-price rule

Truthful single-item auction

puzzle 204▶ ~11 min

Greedy vertex cover×Maximal matching

Vertex cover 2-approximation

Search, Constraints & Games

puzzle 03▶ ~7 min

Minimax×Alpha-beta pruning order

Adversarial game trees

puzzle 04▶ ~7 min

Backtracking search×Minimum remaining values

Sudoku and constraint grids

puzzle 05▶ ~7 min

Branch and bound×Fractional relaxation bound

The 0/1 knapsack

puzzle 06▶ ~8 min

Monte Carlo tree search×UCB1 exploration bonus

Games too big to solve

puzzle 84▶ ~8 min

DPLL×Unit propagation

Boolean satisfiability

puzzle 110▶ ~8 min

Alpha-beta pruning×Iterative deepening move ordering

Game-tree search

puzzle 118▶ ~8 min

Knuth's Algorithm X×Dancing links

Exact cover

puzzle 166▶ ~10 min

Counterfactual regret minimization×Regret-matching updates

Imperfect-information equilibria

puzzle 171▶ ~10 min

Maintaining arc consistency×AC-3 propagation

Constraint satisfaction

puzzle 175▶ ~10 min

Tower of Hanoi×Recursive halving

Disk-transfer puzzle

Strings & Text

puzzle 09▶ ~8 min

Knuth-Morris-Pratt×Failure-function prefixes

Needles in streaming haystacks

puzzle 25▶ ~8 min

Wagner-Fischer×Prefix-to-prefix table

Edit distance, witnessed

puzzle 27▶ ~8 min

Aho-Corasick×Failure-link automaton

Matching many patterns at once

puzzle 44▶ ~8 min

Boyer-Moore×Bad-character and good-suffix rules

Substring search

puzzle 49▶ ~8 min

Suffix array construction×Prefix-doubling ranks

Full-text indexing

puzzle 56▶ ~8 min

Smith-Waterman×Zero-floored local scores

Local sequence alignment

puzzle 66▶ ~8 min

Bitap algorithm×Bitmask fuzzy states

Approximate string matching

puzzle 68▶ ~8 min

Suffix tree×Ukkonen online construction

Full-text indexing

puzzle 79▶ ~8 min

Manacher's algorithm×Mirrored radius reuse

Longest palindromic substring

puzzle 80▶ ~8 min

Z-algorithm×Z-box window reuse

Pattern preprocessing

puzzle 101▶ ~8 min

Rabin-Karp×Rolling hash fingerprints

Fingerprint substring search

puzzle 124▶ ~8 min

Myers diff algorithm×Shortest-edit-script search

Text diffing

Computational Geometry & Topology

puzzle 19▶ ~8 min

Graham scan×Polar-angle sorting

Convex hulls in the plane

puzzle 41▶ ~8 min

Closest pair divide and conquer×Midline strip merge

Closest pair of points

puzzle 83▶ ~8 min

Welzl's algorithm×Randomized incremental basis

Smallest enclosing circle

puzzle 105▶ ~8 min

K-d tree×Median-split axis cycling

Nearest-neighbor search

puzzle 120▶ ~8 min

Bowyer-Watson×Bad-triangle cavity retriangulation

Delaunay triangulation

puzzle 146▶ ~8 min

Douglas-Peucker×Max-deviation recursion

Polyline simplification

puzzle 205▶ ~10 min

Hidden Markov map matching×Emission-transition road probabilities

Map matching

Numerical & Scientific Computing

puzzle 20▶ ~8 min

Gradient descent×Polyak momentum

Smooth minimization

puzzle 28▶ ~8 min

Simplex method×Dantzig pivot rule

Linear programming

puzzle 31▶ ~8 min

Strassen's algorithm×Seven-product block split

Fast matrix multiplication

puzzle 37▶ ~8 min

Fast Fourier transform×Cooley-Tukey radix-2

Spectral analysis

puzzle 45▶ ~8 min

Newton's method×Tangent-line iteration

Root finding

puzzle 55▶ ~8 min

Karatsuba multiplication×Three-product splitting

Big-integer multiplication

puzzle 65▶ ~8 min

Toom-Cook multiplication×Five-point interpolation

Big-integer multiplication

puzzle 112▶ ~8 min

Dormand-Prince×Embedded error step control

Adaptive ODE integration

puzzle 133▶ ~8 min

Gaussian elimination×Partial pivoting

Linear systems

puzzle 137▶ ~8 min

Automatic differentiation×Reverse mode

Gradient computation

puzzle 140▶ ~8 min

Conjugate gradient×Jacobi preconditioner

SPD sparse systems

puzzle 159▶ ~9 min

Barnes-Hut×Octree center-of-mass approximation

N-body simulation

puzzle 160▶ ~9 min

Levenberg-Marquardt×Trust-region damping

Nonlinear least squares

puzzle 161▶ ~9 min

Nelder-Mead×Reflect-expand-contract simplex

Derivative-free optimization

puzzle 167▶ ~10 min

Brent's method×Inverse quadratic interpolation

Robust root finding

Signal, Image & Graphics

puzzle 97▶ ~8 min

Kalman filter×Covariance-weighted correction

Linear state estimation

puzzle 145▶ ~8 min

RANSAC×Random consensus sampling

Robust model fitting

puzzle 153▶ ~9 min

Hough transform×Parameter-space voting

Line detection

puzzle 154▶ ~9 min

Otsu thresholding×Between-class variance

Image binarization

puzzle 173▶ ~10 min

Canny edge detector×Hysteresis thresholding

Edge detection

puzzle 190▶ ~10 min

Connected component labeling×Two-pass union-find

Region labeling

puzzle 191▶ ~11 min

Perlin noise×Gradient lattice interpolation

Procedural texturing

puzzle 200▶ ~10 min

Template matching×Normalized cross-correlation

Pattern localization

Machine Learning & AI

puzzle 18▶ ~8 min

K-means×K-means++ seeding

Clustering points into k groups

puzzle 29▶ ~8 min

Viterbi algorithm×Max-product trellis

Decoding hidden sequences

puzzle 36▶ ~8 min

Metropolis-Hastings×Proposal acceptance ratio

MCMC sampling

puzzle 63▶ ~8 min

Gibbs sampling×Coordinate-wise conditional draws

Posterior sampling

puzzle 103▶ ~8 min

Gaussian mixture model×Expectation-maximization

Soft clustering

puzzle 109▶ ~8 min

Thompson sampling×Posterior draws

Multi-armed bandits

puzzle 126▶ ~8 min

Backpropagation×Stochastic gradient descent

Neural network training

puzzle 127▶ ~8 min

Q-learning×Epsilon-greedy exploration

Reinforcement learning

puzzle 128▶ ~8 min

AdaBoost×Exponential reweighting

Boosted classification

puzzle 129▶ ~8 min

DBSCAN×Density-reachability

Arbitrary-shape clustering

puzzle 130▶ ~8 min

Perceptron×Mistake-driven updates

Linear classification

puzzle 149▶ ~9 min

Decision tree×Information gain splits

Interpretable classification

puzzle 150▶ ~9 min

Naive Bayes×Laplace smoothing

Probabilistic classification

puzzle 151▶ ~9 min

Association rule mining×Apriori candidate pruning

Market-basket analysis

puzzle 152▶ ~9 min

Dynamic time warping×Elastic alignment

Series similarity

puzzle 164▶ ~10 min

Holt-Winters×Triple seasonal smoothing

Seasonal forecasting

puzzle 192▶ ~11 min

Random search×Uniform hyperparameter sampling

Hyperparameter tuning

puzzle 197▶ ~10 min

Gaussian process regression×RBF kernel

Probabilistic regression

Probabilistic, Randomized & Simulation

puzzle 11▶ ~8 min

Bloom filter×K independent hashes

Approximate set membership

puzzle 12▶ ~8 min

HyperLogLog×Leading-zero registers

Counting distinct at scale

puzzle 16▶ ~8 min

Reservoir sampling×Algorithm R

Sampling unbounded streams

puzzle 42▶ ~8 min

MinHash×Bottom-k signatures

Jaccard similarity estimation

puzzle 46▶ ~8 min

Fisher-Yates shuffle×Backward uniform swaps

Uniform permutation

puzzle 54▶ ~8 min

Count-min sketch×Minimum over hash rows

Frequency estimation

puzzle 59▶ ~8 min

Boyer-Moore majority vote×Pairwise cancellation

Majority element

puzzle 64▶ ~8 min

Cuckoo filter×Fingerprint eviction

Deletable set membership

puzzle 70▶ ~8 min

Space-Saving×Min-counter replacement

Top-k heavy hitters

puzzle 136▶ ~8 min

Discrete event simulation×Event-queue advance

Systems modeling

puzzle 176▶ ~10 min

M/M/1 analysis×Birth-death balance equations

Single-queue analysis

puzzle 179▶ ~10 min

Kernel density estimation×Silverman bandwidth

Density estimation

puzzle 182▶ ~10 min

Monte Carlo integration×Uniform sampling

Numerical integration

puzzle 184▶ ~10 min

Bonferroni correction×Family-wise error control

Multiple testing

puzzle 201▶ ~11 min

Importance sampling×Variance-reducing proposal

Rare-event estimation

Cryptography & Number Theory

puzzle 32▶ ~8 min

Miller-Rabin×Witness rounds

Probabilistic primality

puzzle 76▶ ~8 min

Sieve of Eratosthenes×Crossing off from the square

Prime enumeration

puzzle 78▶ ~8 min

Pollard's rho×Floyd cycle detection

Integer factorization

puzzle 88▶ ~8 min

Modular exponentiation×Square-and-multiply

Fast modular powers

puzzle 95▶ ~8 min

Shamir secret sharing×Polynomial interpolation

Threshold secret splitting

puzzle 147▶ ~8 min

Chinese remainder theorem×Garner's algorithm

Modular reconstruction

puzzle 177▶ ~10 min

Differential privacy×Laplace mechanism

Private data release

Information Theory & Coding

puzzle 14▶ ~8 min

Huffman coding×Frequency-sorted merges

Squeezing symbols to their frequencies

puzzle 38▶ ~8 min

Burrows-Wheeler compression×Move-to-front plus RLE

Block-sorting compression

puzzle 86▶ ~8 min

Arithmetic coding×Range renormalization

Near-entropy compression

puzzle 121▶ ~8 min

Reed-Solomon×Berlekamp-Massey decoding

Burst error correction

puzzle 195▶ ~10 min

Shannon entropy estimation×Maximum likelihood plug-in

Entropy estimation

Systems & Networking

puzzle 40▶ ~8 min

Consistent hashing×Virtual nodes

Distributed key placement

puzzle 61▶ ~8 min

Rendezvous hashing×Highest-random-weight

Distributed key placement

puzzle 90▶ ~8 min

Raft×Leader election with terms

Distributed consensus

puzzle 99▶ ~8 min

Chandy-Lamport×Marker-based snapshots

Distributed snapshots

puzzle 114▶ ~8 min

Work stealing×Randomized victim selection

Task-parallel scheduling

puzzle 116▶ ~8 min

Paxos×Proposer-acceptor quorums

Distributed consensus

puzzle 132▶ ~8 min

Banker's algorithm×Safe-state check

Deadlock avoidance

puzzle 143▶ ~8 min

Gossip protocol×Random-peer anti-entropy

Epidemic dissemination

puzzle 144▶ ~8 min

Parallel prefix sum×Blelloch scan

Data-parallel primitive

puzzle 157▶ ~9 min

Garbage collection×Mark and sweep

Automatic memory management

puzzle 158▶ ~9 min

TCP congestion control×AIMD slow start

Congestion avoidance

puzzle 193▶ ~10 min

Distance-vector routing×Bellman-Ford exchange

Network routing

puzzle 202▶ ~11 min

Longest prefix match×Trie lookup

IP forwarding

Databases & Information Retrieval

puzzle 85▶ ~8 min

Hash join×Build-probe partitioning

Equi-join

puzzle 92▶ ~8 min

External merge sort×K-way run merging

Large-relation sorting

puzzle 93▶ ~8 min

Multiversion concurrency control×Snapshot timestamps

Transaction isolation

puzzle 104▶ ~8 min

Log-structured merge tree×Leveled compaction

Write-optimized storage

puzzle 125▶ ~8 min

HNSW×Navigable small-world layers

Vector similarity search

puzzle 141▶ ~8 min

Byte pair encoding×Frequency-merge vocabulary

Subword tokenization

puzzle 148▶ ~8 min

Locality-sensitive hashing×Random hyperplane hashes

Approximate nearest neighbors

puzzle 169▶ ~10 min

BM25 ranking×Saturating term frequency

Document ranking

puzzle 199▶ ~11 min

Formal Languages & Compilers

puzzle 87▶ ~8 min

Subset construction×Powerset determinization

NFA to DFA

puzzle 94▶ ~8 min

Tomasulo's algorithm×Reservation stations with register renaming

Out-of-order execution

puzzle 113▶ ~8 min

Pratt parsing×Binding-power dispatch

Expression parsing

puzzle 119▶ ~8 min

Hopcroft's minimization×Partition refinement

DFA minimization

puzzle 156▶ ~9 min

Binary decision diagram×Reduced ordered canonical form

Boolean function representation

puzzle 162▶ ~10 min

Register allocation×Graph coloring

Compiler backend

puzzle 174▶ ~10 min

Shunting yard×Operator stack

Expression to postfix

puzzle 187▶ ~10 min

Reaching definitions×Forward dataflow

Dataflow analysis

puzzle 194▶ ~11 min

Set-associative cache×Index-tag lookup

Cache organization

puzzle 203▶ ~10 min

LL(1) parsing×First-follow table

Predictive parsing

Quantum & Unconventional Computing

puzzle 134▶ ~8 min

Grover's search×Amplitude amplification

Unstructured search

Computational Biology & Chemistry

puzzle 91▶ ~8 min

Velocity Verlet dynamics×Symplectic time stepping

Molecular dynamics integration

puzzle 96▶ ~8 min

de Bruijn graph assembly×K-mer overlap

Genome assembly

puzzle 196▶ ~11 min

BLAST×Seed-and-extend word matches

Sequence database search

Robotics, Control & Planning

puzzle 115▶ ~8 min

Rapidly-exploring random tree×Voronoi-biased sampling

Motion planning

puzzle 138▶ ~8 min

Monte Carlo localization×Particle filter

Robot localization

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