Cracking the Code

Data Structures & Algorithms for Interviews

A complete DSA curriculum from Big-O and memory models through trees, heaps, and graphs — plus an expanding roadmap of algorithm deep dives that go beyond the interview fundamentals: advanced dynamic programming, divide and conquer, bit manipulation, number theory, and more.

15Core Parts
160Algorithm Topics
10Practical Projects
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12-Part DSA Series + 3 Advanced Guides

Core Series

Master data structures and algorithms for FAANG interviews. From complexity analysis to graphs, dynamic programming, and advanced problem-solving patterns — the exact skills tested at Google, Amazon, Meta, and top tech companies. All 12 parts complete, plus 3 advanced companion guides.

Part 1
Foundations, Memory & Complexity
25 min read
Big OComplexityMemory
Master Big O notation, time/space complexity, memory models, and analysis techniques for algorithm performance.
Read Article →
Part 2
Recursion Complete Guide
22 min read
RecursionCall StackMemoization
Deep dive into recursion, call stack mechanics, tail recursion, memoization, and recursive problem-solving patterns.
Read Article →
Part 3
Arrays & ADT Operations
28 min read
ArraysTwo PointersSliding Window
Arrays, dynamic arrays, two-pointer techniques, sliding window, and essential array manipulation patterns.
Read Article →
Part 4
Strings & Manipulation
26 min read
StringsPattern MatchingKMP
String algorithms, pattern matching, KMP, Rabin-Karp, and common string manipulation interview problems.
Read Article →
Part 5
Matrices & Sparse Arrays
24 min read
Matrices2D ArraysSparse
2D arrays, matrix traversal patterns, sparse matrices, and matrix-based interview problems.
Read Article →
Part 6
Linked Lists Guide
30 min read
Linked ListsPointersCycle Detection
Singly, doubly, circular linked lists, fast/slow pointers, cycle detection, and reversal techniques.
Read Article →
Part 7
Stack & Applications
28 min read
StackMonotonicExpressions
Stack implementation, monotonic stacks, expression evaluation, and stack-based problem patterns.
Read Article →
Part 8
Queue & Implementations
26 min read
QueueDequeBFS
Queue variants, circular queue, deque, priority queue basics, and BFS applications.
Read Article →
Part 9
Trees & Traversals
32 min read
TreesTraversalsDFS/BFS
Binary trees, tree traversals (DFS/BFS), tree construction, and common tree problem patterns.
Read Article →
Part 10
BST & Balanced Trees
35 min read
BSTAVLRed-Black
Binary Search Trees, AVL trees, Red-Black trees, rotations, and self-balancing operations.
Read Article →
Part 11
Heaps, Sorting & Hashing
38 min read
HeapsSortingHashing
Heap operations, heapify, sorting algorithms (merge, quick, heap sort), and hash table implementations.
Read Article →
Part 12
Graphs, DP, Greedy & Backtracking
35 min read
GraphsDPBacktracking
Graph algorithms (BFS, DFS, Dijkstra), dynamic programming patterns, greedy strategies, and backtracking. For a much deeper treatment of graph algorithms specifically, see the dedicated Graph Theory series.
Read Article →
Advanced
Amortized Analysis & Dynamic Array Growth
14 min read
AmortizedAnalysisDynamic Array
Aggregate, accounting, and potential methods — proving O(1) amortized append and why doubling vs linear growth matters.
Read Article →
Advanced
Union-Find, Trie, Fenwick & Segment Tree
18 min read
Union-FindTrieSegment Tree
Decision guide and full implementations for four advanced structures that unlock hard interview problems.
Read Article →
Advanced
Interview Pattern Recognition Guide
16 min read
PatternsFAANGInterview Prep
Map 14 algorithm patterns to problem keywords: two-pointer, sliding window, BFS, DP, monotonic stack, heap, and more.
Read Article →
14 Levels + 160 Topics

Algorithm Master Curriculum

The complete non-graph algorithm roadmap, expanded from foundations through advanced data structures, dynamic programming, strings, mathematics, geometry, systems, parallel algorithms, and optimization. Graph-specific material remains in the dedicated Graph Theory series.

13 Curriculum Topics

Level 1 — Foundations

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 1
Algorithm Analysis
Curriculum Topic
CorrectnessLoop invariantsTime
Correctness · Loop invariants · Time/space complexity · Best/average/worst case Amortized analysis · Recurrences · Master Theorem · Akra-Bazzi · Lower bounds Comparison-model lower bounds · Expected randomized complexity · Cache awareness
Read Lesson →
Algorithm 2
Fundamental Sorting
Curriculum Topic
BubbleInsertionSelection
Bubble · Insertion · Selection · Merge · Quick · Heap · Counting · Radix · Bucket Shell · Comb · Cocktail · Gnome · Cycle · Pigeonhole
Read Lesson →
Algorithm 3
Practical / Hybrid Sorting
Curriculum Topic
TimsortIntrosortDual-Pivot Quicksort
Timsort · Introsort · Dual-Pivot Quicksort · External Merge Sort Multiway Merge · Bitonic Sort · Odd-Even Merge Sort · Sorting Networks
Read Lesson →
Algorithm 4
Searching
Curriculum Topic
Linear SearchBinary SearchLower
Linear Search · Binary Search · Lower/Upper Bound · First/Last Occurrence Binary Search on Answer · Binary Search on Reals · Ternary Search Jump Search · Exponential Search · Interpolation Search · Fibonacci Search Galloping Search
Read Lesson →
Algorithm 5
Selection / Order Statistics
Curriculum Topic
QuickselectRandomized QuickselectMedian of Medians
Quickselect · Randomized Quickselect · Median of Medians / BFPRT k-th Smallest/Largest · Top-k with Heap · Partial Sort · Weighted Median Streaming Median with Two Heaps
Read Lesson →
Algorithm 6
Two Pointers
Curriculum Topic
Pair Sum3-Sum4-Sum patterns
Pair Sum · 3-Sum / 4-Sum patterns · Remove Duplicates · Move Zeroes Container With Most Water · Partitioning · Opposite/Same Direction Pointers
Read Lesson →
Algorithm 7
Sliding Window
Curriculum Topic
Fixed WindowVariable WindowLongest
Fixed Window · Variable Window · Longest/Shortest Valid Subarray Frequency Windows · Minimum Window Substring · K-Distinct Windows Sliding Window Max/Min · Sliding Median
Read Lesson →
Algorithm 8
Prefix / Difference Techniques
Curriculum Topic
1D2D Prefix SumsPrefix XOR
1D/2D Prefix Sums · Prefix XOR · Prefix Frequency 1D/2D Difference Arrays · Imos Method · Range Update Reconstruction
Read Lesson →
Algorithm 9
Hashing
Curriculum Topic
Hash TablesSetsFrequency Counting
Hash Tables/Sets · Frequency Counting · Two Sum · Subarray Sum Anagrams · Custom Hashing · Chaining/Open Addressing · Universal Hashing
Read Lesson →
Algorithm 10
Recursion / Backtracking Basics
Curriculum Topic
FactorialFibonacciSubsets
Factorial/Fibonacci · Subsets · Permutations · Combinations Combination Sum · Generate Parentheses · N-Queens · Word Search Choice-Constraint-Undo Pattern
Read Lesson →
Algorithm 11
Stacks / Queues / Deques
Curriculum Topic
Valid ParenthesesMin StackExpression Evaluation Infix
Valid Parentheses · Min Stack · Expression Evaluation Infix/Prefix/Postfix · Next/Previous Greater/Smaller · Stock Span Monotonic Stack · Circular Queue · Ring Buffer · Monotonic Deque
Read Lesson →
Algorithm 12
Linked-List Algorithms
Curriculum Topic
InsertDeleteReverse
Insert/Delete · Reverse · Reverse in Groups · Merge Sorted Lists Find Middle · Floyd Cycle Detection · Find Cycle Entry Remove N-th from End · Intersection · Palindrome Check Merge Sort on Lists · LRU Cache · Skip List
Read Lesson →
Algorithm 13
Bit Manipulation
Curriculum Topic
SetClearToggle
Set/Clear/Toggle/Test Bits · Popcount · Kernighan Trick · Parity Power-of-Two · Lowest Set Bit · XOR Tricks · Gray Code Bit Reversal · CLZ/CTZ · Bit Packing · Morton/Z-order Basics
Read Lesson →
13 Curriculum Topics

Level 2 — Tree Data Structures And Tree Algorithms

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 14
Binary Trees
Curriculum Topic
PreorderInorderPostorder
Preorder · Inorder · Postorder · Level Order · Iterative Traversals Height · Node/Leaf Count · Equality · Mirror/Invert
Read Lesson →
Algorithm 15
Advanced Binary-Tree Traversal
Curriculum Topic
Morris InorderMorris PreorderThreaded Trees Boundary Trav
Morris Inorder · Morris Preorder · Threaded Trees Boundary Traversal · Zigzag Traversal · Vertical-Order Concepts Serialization/Deserialization · Reconstruct from Traversals
Read Lesson →
Algorithm 16
Binary Search Trees
Curriculum Topic
SearchInsertDelete
Search · Insert · Delete · Min/Max · Predecessor/Successor Floor/Ceiling · Range Search · Validate BST · Balanced Build · BST Iterator
Read Lesson →
Algorithm 17
Self-Balancing BSTs
Curriculum Topic
AVL TreesRotationsRed-Black Trees
AVL Trees · Rotations · Red-Black Trees · Insert/Delete Fix-Up 2-3 Trees · 2-3-4 Trees · Weight-Balanced Trees
Read Lesson →
Algorithm 18
Randomized / Self-Adjusting Trees
Curriculum Topic
TreapSplitMerge Treap
Treap · Split/Merge Treap · Implicit Treap · Randomized BST Splay Tree · Splaying · Working-Set Intuition
Read Lesson →
Algorithm 19
Order-Statistic Trees
Curriculum Topic
Subtree-Size AugmentationSelect k-thRank
Subtree-Size Augmentation · Select k-th · Rank · Dynamic Order Statistics
Read Lesson →
Algorithm 20
Multiway Search Trees
Curriculum Topic
B-TreeB-Tree SearchInsert
B-Tree · B-Tree Search/Insert/Delete · B+ Tree · B+ Range Scans Database/Filesystem Index Applications
Read Lesson →
Algorithm 21
Heap Structures
Curriculum Topic
Binary MinMax HeapHeapify
Binary Min/Max Heap · Heapify · Build Heap · Insert/Extract Decrease/Increase Key · d-ary Heap · Min-Max Heap · Indexed PQ
Read Lesson →
Algorithm 22
Advanced Heaps
Curriculum Topic
Binomial HeapFibonacci HeapPairing Heap
Binomial Heap · Fibonacci Heap · Pairing Heap · Leftist Heap · Skew Heap Meldable Heaps
Read Lesson →
Algorithm 23
Cartesian Trees
Curriculum Topic
O(n) Monotonic-Stack ConstruMinMax Cartesian Trees RMQ Conn
O(n) Monotonic-Stack Construction · Min/Max Cartesian Trees RMQ Connection · Treap Connection
Read Lesson →
Algorithm 24
Expression / Syntax Trees
Curriculum Topic
Expression Tree ConstructionEvaluationAST Basics Recursive Tree Ev
Expression Tree Construction · Evaluation · AST Basics Recursive Tree Evaluation
Read Lesson →
Algorithm 25
Interval / Range Trees
Curriculum Topic
Interval TreeOverlap QueriesRange Tree
Interval Tree · Overlap Queries · Range Tree · Augmented BST
Read Lesson →
Algorithm 26
Persistent / Functional Trees
Curriculum Topic
Path CopyingPersistent BSTTreap
Path Copying · Persistent BST/Treap · Persistent Segment Tree Persistent Trie · Finger Trees Overview
Read Lesson →
10 Curriculum Topics

Level 3 — Range Queries And Sequence Data Structures

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 27
Monotonic Structures
Curriculum Topic
Monotonic StackQueueDeque
Monotonic Stack/Queue/Deque · Histogram Largest Rectangle Maximal Rectangle · Trapping Rain Water · Next/Previous Extremum
Read Lesson →
Algorithm 28
Coordinate Compression
Curriculum Topic
Rank CompressionStable MappingDuplicate Handling
Rank Compression · Stable Mapping · Duplicate Handling
Read Lesson →
Algorithm 29
Offline Query Processing
Curriculum Topic
Sort-by-ThresholdEvent SortingSweep Processing Offline Cou
Sort-by-Threshold · Event Sorting · Sweep Processing Offline Counting · Inversion Counting
Read Lesson →
Algorithm 30
Square-Root Decomposition
Curriculum Topic
Block DecompositionPoint UpdateRange Query
Block Decomposition · Point Update/Range Query · Range Update Variants
Read Lesson →
Algorithm 31
Mo's Algorithm
Curriculum Topic
Standard MoAddRemove Maintenance
Standard Mo · Add/Remove Maintenance · Mo with Modifications Hilbert-Order Optimization
Read Lesson →
Algorithm 32
Fenwick Tree / BIT
Curriculum Topic
Point UpdatePrefix QueryRange Update
Point Update/Prefix Query · Range Update/Point Query Range Update/Range Query · Order Statistics · 2D BIT
Read Lesson →
Algorithm 33
Segment Tree
Curriculum Topic
RecursiveIterativePoint
Recursive/Iterative · Point/Range Query · Lazy Propagation Segment Tree Beats · Merge-Sort Tree · Persistent Segment Tree Dynamic/Implicit Segment Tree · 2D Segment Tree
Read Lesson →
Algorithm 34
Sparse Tables
Curriculum Topic
Sparse TableRMQGCD
Sparse Table · RMQ · GCD/Max/Min · Disjoint Sparse Table
Read Lesson →
Algorithm 35
Wavelet Structures
Curriculum Topic
Wavelet TreeWavelet MatrixRange k-th
Wavelet Tree · Wavelet Matrix · Range k-th · Rank/Select · Range Frequency
Read Lesson →
Algorithm 36
Succinct Structures
Curriculum Topic
BitvectorsRankSelect
Bitvectors · Rank/Select · Succinct Sequence Basics · FM-index Foundations
Read Lesson →
21 Curriculum Topics

Level 4 — Dynamic Programming

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 37
DP Foundations
Curriculum Topic
MemoizationTabulationState
Memoization · Tabulation · State/Transition Design · Reconstruction Space Optimization
Read Lesson →
Algorithm 38
1D DP
Curriculum Topic
Fibonacci PatternsHouse RobberMin-Cost Progression
Fibonacci Patterns · House Robber · Min-Cost Progression · Kadane
Read Lesson →
Algorithm 39
Knapsack Family
Curriculum Topic
01Unbounded
0/1 · Unbounded · Bounded · Multiple Knapsack Subset Sum · Partition · Bitset Optimization
Read Lesson →
Algorithm 40
Coin Change
Curriculum Topic
Minimum CoinsNumber of WaysOrdered Compositions
Minimum Coins · Number of Ways · Ordered Compositions · Bounded Coins
Read Lesson →
Algorithm 41
Sequence DP
Curriculum Topic
LCSLongest Common SubstringEdit Distance
LCS · Longest Common Substring · Edit Distance · Damerau-Levenshtein Shortest Common Supersequence · Longest Palindromic Subsequence
Read Lesson →
Algorithm 42
LIS Family
Curriculum Topic
O(n^2) LISO(n log n) Patience MethodReconstruction
O(n^2) LIS · O(n log n) Patience Method · Reconstruction · Count LIS Decreasing/Bitonic/Maximum-Sum Increasing Subsequences
Read Lesson →
Algorithm 43
Grid DP
Curriculum Topic
Path CountingMinimum CostObstacles
Path Counting · Minimum Cost · Obstacles · Multi-State Grid DP
Read Lesson →
Algorithm 44
Interval DP
Curriculum Topic
Matrix Chain MultiplicationBurst BalloonsOptimal BST Palindrome Parti
Matrix Chain Multiplication · Burst Balloons · Optimal BST Palindrome Partition · Interval Merge DP
Read Lesson →
Algorithm 45
Bitmask DP
Curriculum Topic
Subset StatesAssignment DPSet Partition DP
Subset States · Assignment DP · Set Partition DP · Submask Enumeration
Read Lesson →
Algorithm 46
SOS DP
Curriculum Topic
Zeta TransformMöbius TransformSubmask
Zeta Transform · Möbius Transform · Submask/Supermask Sums OR/AND/XOR Transform Connections
Read Lesson →
Algorithm 47
Profile / Broken-Profile DP
Curriculum Topic
TilingRowColumn Masks
Tiling · Row/Column Masks · Plug/Profile DP · Transfer-Matrix View
Read Lesson →
Algorithm 48
Rooted/Binary-Tree DP
Curriculum Topic
Postorder State AggregationIncludeExclude States Binary-Tree H
Postorder State Aggregation · Include/Exclude States Binary-Tree House-Robber Pattern · BST-Shape DP · Tree Knapsack Patterns
Read Lesson →
Algorithm 49
Probability / Expectation DP
Curriculum Topic
Expected ValueProbability TransitionsExpected Stopping Time
Expected Value · Probability Transitions · Expected Stopping Time
Read Lesson →
Algorithm 50
Game DP
Curriculum Topic
WinningLosing StatesMinimax on Finite State Tree
Winning/Losing States · Minimax on Finite State Trees · Interval Games
Read Lesson →
Algorithm 51
Monotonic-Queue DP Optimization
Curriculum Topic
Sliding Transition WindowsDeque Optimization
Sliding Transition Windows · Deque Optimization
Read Lesson →
Algorithm 52
Divide-and-Conquer DP Optimization
Curriculum Topic
Monotone Opt IndicesD&C Optimization Template
Monotone Opt Indices · D&C Optimization Template
Read Lesson →
Algorithm 53
Knuth Optimization
Curriculum Topic
Quadrangle InequalityMonotone Optima
Quadrangle Inequality · Monotone Optima
Read Lesson →
Algorithm 54
Convex Hull Trick / Li Chao
Curriculum Topic
Monotone HullDynamic HullLi Chao Tree
Monotone Hull · Dynamic Hull · Li Chao Tree · Compressed Li Chao
Read Lesson →
Algorithm 55
Monge / SMAWK
Curriculum Topic
Monge ArraysTotally Monotone MatricesSMAWK
Monge Arrays · Totally Monotone Matrices · SMAWK
Read Lesson →
Algorithm 56
Aliens Trick / Lagrangian DP
Curriculum Topic
Penalty SearchWQS Binary SearchExact-Count Recovery
Penalty Search · WQS Binary Search · Exact-Count Recovery
Read Lesson →
Algorithm 57
Bitset DP
Curriculum Topic
Fast Boolean State TransitioSubset SumString DP Acceleration
Fast Boolean State Transitions · Subset Sum · String DP Acceleration
Read Lesson →
8 Curriculum Topics

Level 5 — Greedy / Divide And Conquer

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 58
Greedy Proof Techniques
Curriculum Topic
Exchange ArgumentStaying AheadGreedy Choice
Exchange Argument · Staying Ahead · Greedy Choice
Read Lesson →
Algorithm 59
Interval Scheduling
Curriculum Topic
Activity SelectionInterval PartitioningMinimum Rooms Interval Cover
Activity Selection · Interval Partitioning · Minimum Rooms Interval Covering · Maximum Non-Overlap
Read Lesson →
Algorithm 60
Scheduling Greedy
Curriculum Topic
Job SequencingMoore-HodgsonSmith's Rule Earliest Deadli
Job Sequencing · Moore-Hodgson · Smith's Rule Earliest Deadline First · Shortest Processing Time
Read Lesson →
Algorithm 61
Fractional Knapsack
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 62
Greedy Arrays
Curriculum Topic
Gas StationJump GameCandy
Gas Station · Jump Game · Candy · Interval Stabbing Merge Intervals · Partition Labels
Read Lesson →
Algorithm 63
Divide and Conquer
Curriculum Topic
Merge Sort ApplicationsInversion CountReverse Pairs Quicksort Part
Merge Sort Applications · Inversion Count · Reverse Pairs Quicksort Partitions · Quickselect
Read Lesson →
Algorithm 64
Matrix Divide and Conquer
Curriculum Topic
Strassen Matrix Multiplicati
Strassen Matrix Multiplication
Read Lesson →
Algorithm 65
CDQ Divide and Conquer
Curriculum Topic
Offline CountingDPQuery Applications
Offline Counting · DP/Query Applications
Read Lesson →
12 Curriculum Topics

Level 6 — Combinatorics / Polynomials

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 66
nCr / Pascal Triangle
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 67
Inclusion-Exclusion
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 68
Catalan Numbers
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 69
Stirling Numbers
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 70
Bell Numbers
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 71
Derangements
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 72
Integer Partitions
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 73
Stars and Bars
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 74
Burnside's Lemma
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 75
Pólya Enumeration
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 76
Combinatorial Transforms
Curriculum Topic
BinomialMöbiusZeta
Binomial · Möbius · Zeta
Read Lesson →
Algorithm 77
Fast Walsh-Hadamard Transform
Curriculum Topic
XORANDOR Convolution
XOR · AND · OR Convolution
Read Lesson →
17 Curriculum Topics

Level 7 — Linear Algebra / Numerical Methods

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 78
Matrix Operations / Sparse Matrices
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 79
Matrix Exponentiation
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 80
Gaussian Elimination
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 81
Gauss-Jordan
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 82
LU Decomposition
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 83
QR Decomposition
Curriculum Topic
Gram-SchmidtHouseholderGivens
Gram-Schmidt · Householder · Givens
Read Lesson →
Algorithm 84
Cholesky Decomposition
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 85
Eigenvalue Methods
Curriculum Topic
Power IterationInverse IterationQR Algorithm
Power Iteration · Inverse Iteration · QR Algorithm
Read Lesson →
Algorithm 86
Singular Value Decomposition
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 87
GF(2) Gaussian Elimination / XOR Basis
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 88
Root Finding
Curriculum Topic
BisectionNewton-RaphsonSecant
Bisection · Newton-Raphson · Secant · Regula Falsi · Brent
Read Lesson →
Algorithm 89
Numerical Integration
Curriculum Topic
TrapezoidalSimpsonAdaptive Simpson
Trapezoidal · Simpson · Adaptive Simpson · Gaussian Quadrature · Monte Carlo
Read Lesson →
Algorithm 90
Numerical Differentiation
Curriculum Topic
ForwardBackwardCentral Difference
Forward/Backward/Central Difference · Richardson
Read Lesson →
Algorithm 91
Interpolation
Curriculum Topic
LagrangeNewton Divided DifferenceCubic Spline
Lagrange · Newton Divided Difference · Cubic Spline
Read Lesson →
Algorithm 92
ODE Solvers
Curriculum Topic
EulerHeunRK4
Euler · Heun · RK4 · Adaptive Runge-Kutta
Read Lesson →
Algorithm 93
Iterative Linear Solvers
Curriculum Topic
JacobiGauss-SeidelSOR
Jacobi · Gauss-Seidel · SOR · Conjugate Gradient · GMRES
Read Lesson →
Algorithm 94
Numerical Stability
Curriculum Topic
Floating-Point ErrorCancellationKahan Summation
Floating-Point Error · Cancellation · Kahan Summation
Read Lesson →
7 Curriculum Topics

Level 8 — Randomized / Probabilistic Algorithms

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 95
Randomized Quicksort / Quickselect
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 96
Fisher-Yates Shuffle
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 97
Cuckoo Hashing
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 98
Robin Hood Hashing
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 99
Perfect Hashing / FKS
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 100
Randomized Data Structures
Curriculum Topic
TreapSkip List
Treap · Skip List
Read Lesson →
Algorithm 101
Monte Carlo / Las Vegas Algorithms
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
8 Curriculum Topics

Level 9 — Backtracking / Exact / Constraint Algorithms

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 102
Advanced Backtracking
Curriculum Topic
Optimized N-QueensSudokuWord Search
Optimized N-Queens · Sudoku · Word Search · Symmetry Breaking
Read Lesson →
Algorithm 103
Constraint Satisfaction
Curriculum Topic
Forward CheckingPropagationMRV
Forward Checking · Propagation · MRV · Degree Heuristic · LCV
Read Lesson →
Algorithm 104
Exact Cover
Curriculum Topic
Algorithm XDancing Links
Algorithm X · Dancing Links
Read Lesson →
Algorithm 105
SAT Solving
Curriculum Topic
DPLLUnit PropagationPure Literals
DPLL · Unit Propagation · Pure Literals · Watched Literals CDCL · Clause Learning · VSIDS · Restarts
Read Lesson →
Algorithm 106
Branch and Bound
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 107
Meet-in-the-Middle
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 108
Generic Iterative Deepening on Search Trees
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 109
Game-Tree Search
Curriculum Topic
MinimaxAlpha-BetaMove Ordering
Minimax · Alpha-Beta · Move Ordering · Iterative Deepening Transposition Tables · Quiescence Search
Read Lesson →
13 Curriculum Topics

Level 10 — Optimization

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 110
Unimodal Optimization
Curriculum Topic
Ternary SearchGolden-Section Search
Ternary Search · Golden-Section Search
Read Lesson →
Algorithm 111
Hill Climbing / Random Restart
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 112
Simulated Annealing
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 113
Genetic Algorithms
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 114
Differential Evolution
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 115
Particle Swarm Optimization
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 116
Gradient Descent
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 117
SGD / Mini-Batch SGD
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 118
Momentum / Nesterov
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 119
AdaGrad / RMSProp / Adam
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 120
Convex Optimization
Curriculum Topic
SubgradientProjected GradientCoordinate Descent
Subgradient · Projected Gradient · Coordinate Descent · Proximal Gradient
Read Lesson →
Algorithm 121
Linear Programming
Curriculum Topic
SimplexRevised Simplex ConceptsInterior-Point Overview
Simplex · Revised Simplex Concepts · Interior-Point Overview
Read Lesson →
Algorithm 122
Integer Programming
Curriculum Topic
Branch-and-BoundCutting PlanesGeneric Branch-and-Cut
Branch-and-Bound · Cutting Planes · Generic Branch-and-Cut
Read Lesson →
4 Curriculum Topics

Level 11 — Compression / Coding

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 123
Delta / Variable-Byte Encoding
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 124
ANS / Asymmetric Numeral Systems Overview
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 125
Checksums
Curriculum Topic
FletcherAdler-32CRC
Fletcher · Adler-32 · CRC
Read Lesson →
Algorithm 126
Error-Correcting Codes
Curriculum Topic
HammingReed-Solomon OverviewBCH Overview
Hamming · Reed-Solomon Overview · BCH Overview
Read Lesson →
9 Curriculum Topics

Level 12 — External Memory / Systems

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 127
External Merge Sort
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 128
Replacement Selection
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 129
K-Way Merge
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 130
B/B+ Tree External-Memory Search
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 131
Cache-Aware Blocking / Tiling
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 132
Cache-Oblivious Divide-and-Conquer
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 133
van Emde Boas Layout
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 134
Memory Allocation
Curriculum Topic
First FitBest FitWorst Fit
First Fit · Best Fit · Worst Fit · Buddy Allocation · Slab Concepts
Read Lesson →
Algorithm 135
Cache Replacement
Curriculum Topic
LRULFUFIFO
LRU · LFU · FIFO · Clock/Second Chance · ARC Overview
Read Lesson →
11 Curriculum Topics

Level 13 — Parallel / Concurrent / Online

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 136
Parallel Algorithm Analysis
Curriculum Topic
WorkSpanSpeedup
Work · Span · Speedup · Amdahl
Read Lesson →
Algorithm 137
Parallel Prefix / Scan
Curriculum Topic
Hillis-SteeleBlelloch
Hillis-Steele · Blelloch
Read Lesson →
Algorithm 138
Parallel Reduction
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 139
Parallel Sorting
Curriculum Topic
Parallel MergeQuickBitonic
Parallel Merge/Quick · Bitonic · Sample Sort
Read Lesson →
Algorithm 140
Parallel Matrix Multiplication
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 141
Concurrent Data Structures
Curriculum Topic
CASLock-Free StackMichael-Scott Queue
CAS · Lock-Free Stack · Michael-Scott Queue · ABA · Hazard Pointers
Read Lesson →
Algorithm 142
Online Algorithms
Curriculum Topic
Competitive AnalysisAdversarial Inputs
Competitive Analysis · Adversarial Inputs
Read Lesson →
Algorithm 143
Paging / Caching
Curriculum Topic
LRUFIFOBelady OPT
LRU · FIFO · Belady OPT
Read Lesson →
Algorithm 144
Online Scheduling / Load Balancing
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 145
Secretary Problem
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 146
Online Learning
Curriculum Topic
Multiplicative WeightsHedgeFTL
Multiplicative Weights · Hedge · FTL · FTRL
Read Lesson →
14 Curriculum Topics

Level 14 — Advanced Data Structures / Techniques

A complete, ordered checklist of algorithms and techniques in this level.

Algorithm 147
van Emde Boas Tree
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 148
Fusion Trees — Conceptual
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 149
Rope
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 150
Gap Buffer / Piece Table
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 151
Persistent Data Structures
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 152
Functional Queues / Finger Trees
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 153
Priority Search Tree
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 154
Binary Lifting for Non-Graph Function Iteration
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 155
Doubling Technique
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 156
Small-to-Large Merging (non-graph uses)
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 157
Parallel Binary Search
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 158
Rollback Data Structures
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 159
Slope Trick
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
Algorithm 160
Aliens Trick / WQS
Curriculum Topic
Implementation, analysis, and practical applications.
Read Lesson →
10 Master Projects

Practical Project Sequence

Build these projects in order to turn the curriculum into working libraries, toolkits, solvers, and systems.

Project 161
Sorting Laboratory
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 162
Search / Selection Toolkit
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 163
Tree Data-Structure Library
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 164
Heap and Priority-Queue Library
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 165
Range-Query Engine
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 166
Dynamic Programming Workbook
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 167
Exact-Cover / SAT Solver
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 168
Numerical Methods Toolkit
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 169
External-Memory B+ Tree / Sorting Project
Build Project
Implementation, analysis, and practical applications.
Read Lesson →
Project 170
Parallel Prefix / Sorting Project
Build Project
Implementation, analysis, and practical applications.
Read Lesson →