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Volume 1Fundamental Algorithms0 / 18
01
The Notion of an AlgorithmVol. 1, §1.1
02
Mathematical PreliminariesVol. 1, §1.2
03
Information StructuresVol. 1, Ch. 2
18
MMIX: Knuth's MachineVol. 1, Fascicle 1
Volume 2Seminumerical Algorithms0 / 21
04
Random NumbersVol. 2, Ch. 3
05
ArithmeticVol. 2, Ch. 4
12
The Spectral TestVol. 2, §3.3.4
16
The Spectral Test in Higher DimensionsVol. 2, §3.3.4, Algorithm S
19
Floating-Point ArithmeticVol. 2, §4.2
Volume 3Sorting and Searching0 / 22
06
SortingVol. 3, Ch. 5
07
SearchingVol. 3, Ch. 6
11
Multiway Trees and Digital SearchingVol. 3, §6.2.4 & §6.3
15
External SortingVol. 3, §5.4
20
Optimum Sorting and Sorting NetworksVol. 3, §5.3
Volume 4ACombinatorial Algorithms, Part 10 / 17
08
Combinatorial GenerationVol. 4A, §7.2.1
13
Bitwise Tricks and Binary Decision DiagramsVol. 4A, §7.1.3–7.1.4
17
ZDDs and Exact Covering with ColorsVol. 4A, §7.1.4 & Vol. 4B, §7.2.2.1
21
Boolean Functions and Optimal EvaluationVol. 4A, §7.1.1–7.1.2
Volume 4BCombinatorial Algorithms, Part 20 / 12
09
Backtracking and Dancing LinksVol. 4B, §7.2.2–7.2.2.1
10
SatisfiabilityVol. 4B, §7.2.2.2
14
Conflict-Driven Clause LearningVol. 4B, §7.2.2.2, Algorithm C
Toward Volume 4CPre-fascicles0 / 4
22
Hamiltonian Paths and Constraint SatisfactionToward Vol. 4C, §7.2.2.4 (pre-fascicles)
The toolkit you build
The course's real syllabus isn't the algorithms — it's the reasoning. Each proof technique recurs across modules; seen three times, it becomes yours.
| Technique | Met in | Recurs across modules |
|---|---|---|
| Invariant + termination | 01 | 05 · 06 · 07 · 09 · 14 |
| Mathematical induction | 02 | 03 · 04 · 06 · 13 |
| Double counting | 02 | 06 · 08 · 13 |
| Expectation & harmonic sums | 02 | 06 · 07 |
| Extremal witness | 01 | 06 · 07 · 13 · 20 |
| Information-theoretic bound | 06 | 07 · 20 |
| Honest probabilistic analysis | 04 | 05 · 12 · 16 · 19 |
| Lattice / number-theoretic structure | 01 | 04 · 05 · 12 · 16 |
| Reduction between problems | 09 | 10 · 14 · 17 · 22 |
| Amortized / potential | 03 | 07 · 14 · 15 |
| Certification | 01 | 10 · 14 |