''The Art of Computer Programming'' (''TAOCP'') is a comprehensive

monograph A monograph is a specialist work of writing (in contrast to reference works) or exhibition on a single subject or an aspect of a subject, often by a single author or artist, and usually on a scholarly subject. In library cataloging, ''monograph ...

written by the computer scientist Donald Knuth presenting programming

algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s and their analysis. Volumes 1–5 are intended to represent the central core of computer programming for sequential machines. When Knuth began the project in 1962, he originally conceived of it as a single book with twelve chapters. The first three volumes of what was then expected to be a seven-volume set were published in 1968, 1969, and 1973. Work began in earnest on Volume 4 in 1973, but was suspended in 1977 for work on typesetting prompted by the second edition of Volume 2. Writing of the final copy of Volume 4A began in longhand in 2001, and the first online pre-fascicle, 2A, appeared later in 2001. The first published installment of Volume 4 appeared in paperback as

Fascicle Fascicle or ''fasciculus'' may refer to: Anatomy and histology * Muscle fascicle, a bundle of skeletal muscle fibers * Nerve fascicle, a bundle of axons (nerve fibers) ** Superior longitudinal fasciculus *** Arcuate fasciculus ** Gracile fas ...

2 in 2005. The hardback Volume 4A, combining Volume 4, Fascicles 0–4, was published in 2011. Volume 4, Fascicle 6 ("Satisfiability") was released in December 2015; Volume 4, Fascicle 5 ("Mathematical Preliminaries Redux; Backtracking; Dancing Links") was released in November 2019. Volume 4B consists of material evolved from Fascicles 5 and 6. The manuscript was sent to the publisher on August 1, 2022, and the volume was published in September 2022. Fascicle 7, planned for Volume 4C, was the subject of Knuth's talk on August 3, 2022.

History

After winning a Westinghouse Talent Search scholarship, Knuth enrolled at the Case Institute of Technology (now

Case Western Reserve University Case Western Reserve University (CWRU) is a private research university in Cleveland, Ohio. Case Western Reserve was established in 1967, when Western Reserve University, founded in 1826 and named for its location in the Connecticut Western Reser ...

), where his performance was so outstanding that the faculty voted to award him a

master of science A Master of Science ( la, Magisterii Scientiae; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to ...

upon his completion of the

bachelor's degree A bachelor's degree (from Middle Latin ''baccalaureus'') or baccalaureate (from Modern Latin ''baccalaureatus'') is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six ...

. During his summer vacations, Knuth was hired by the Burroughs Corporation to write

compiler In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that ...

s, earning more in his summer months than full professors did for an entire year. Such exploits made Knuth a topic of discussion among the mathematics department, which included Richard S. Varga. In January 1962, when he was a graduate student in the mathematics department at Caltech, Knuth was approached by

Addison-Wesley Addison-Wesley is an American publisher of textbooks and computer literature. It is an imprint of Pearson PLC, a global publishing and education company. In addition to publishing books, Addison-Wesley also distributes its technical titles through ...

to write a book about compiler design, and he proposed a larger scope. He came up with a list of twelve chapter titles the same day. In the summer of 1962 he worked on a FORTRAN compiler for UNIVAC. During this time, he also came up with a mathematical analysis of linear probing, which convinced him to present the material with a quantitative approach. After receiving his Ph.D. in June 1963, he began working on his manuscript, of which he finished his first draft in June 1965, at hand-written pages. He had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about hand-written pages translated to one printed page. This meant he had approximately printed pages of material, which closely matches the size of the first three published volumes. At this point, Knuth received support from Richard S. Varga, who was the scientific adviser to the publisher. Varga was visiting Olga Taussky-Todd and

John Todd John Todd or Tod may refer to: Clergy *John Todd (abolitionist) (1818–1894), preacher and 'conductor' on the Underground Railroad * John Todd (author) (1800–1873), American minister and author * John Todd (bishop), Anglican bishop in the early ...

Caltech The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

. With Varga's enthusiastic endorsement, the publisher accepted Knuth's expanded plans. In its expanded version, the book would be published in seven volumes, each with just one or two chapters. Due to the growth in Chapter 7, which was fewer than 100 pages of the 1965 manuscript, per Vol. 4A p. vi, the plan for Volume 4 has since expanded to include Volumes 4A, 4B, 4C, 4D, and possibly more. In 1976, Knuth prepared a second edition of Volume 2, requiring it to be typeset again, but the style of type used in the first edition (called

hot type ''Hot Type'' was a Canadian television series, which aired weekly on CBC Newsworld. Hosted by Evan Solomon, the program was a cultural talk and interview show focused primarily on books and literature."TV takes new look at the printed word". ''Th ...

) was no longer available. In 1977, he decided to spend some time creating something more suitable. Eight years later, he returned with T_EX, which is currently used for all volumes. The offer of a so-called Knuth reward check worth "one hexadecimal dollar" (100_HEX

base 16 In mathematics and computing, the hexadecimal (also base-16 or simply hex) numeral system is a positional numeral system that represents numbers using a radix (base) of 16. Unlike the decimal system representing numbers using 10 symbols, he ...

cents, in

decimal The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral ...

, is $2.56) for any errors found, and the correction of these errors in subsequent printings, has contributed to the highly polished and still-authoritative nature of the work, long after its first publication. Another characteristic of the volumes is the variation in the difficulty of the exercises. Knuth even has a numerical difficulty scale for rating those exercises, varying from 0 to 50, where 0 is trivial, and 50 is an open question in contemporary research. Knuth's dedication reads:

This series of books is affectionately dedicated
to the Type 650 computer once installed at
Case Institute of Technology,
with whom I have spent many pleasant evenings.The dedication was worded slightly differently in the first edition.

Assembly language in the book

All examples in the books use a language called "

MIX Mix, mixes or mixing may refer to: Persons & places * Mix (surname) ** Tom Mix (1880-1940), American film star * nickname of Mix Diskerud (born Mikkel, 1990), Norwegian-American soccer player * Mix camp, an informal settlement in Namibia * Mix ...

assembly language", which runs on the hypothetical MIX computer. Currently, the MIX computer is being replaced by the

MMIX MMIX (pronounced ''em-mix'') is a 64-bit reduced instruction set computing (RISC) architecture designed by Donald Knuth, with significant contributions by John L. Hennessy (who contributed to the design of the MIPS architecture) and Richard L. S ...

computer, which is a

RISC In computer engineering, a reduced instruction set computer (RISC) is a computer designed to simplify the individual instructions given to the computer to accomplish tasks. Compared to the instructions given to a complex instruction set comput ...

version. Software such as

GNU MDK GNU () is an extensive collection of free software (383 packages as of January 2022), which can be used as an operating system or can be used in parts with other operating systems. The use of the completed GNU tools led to the family of operat ...

exists to provide emulation of the MIX architecture. Knuth considers the use of

assembly language In computer programming, assembly language (or assembler language, or symbolic machine code), often referred to simply as Assembly and commonly abbreviated as ASM or asm, is any low-level programming language with a very strong correspondence be ...

necessary for the speed and memory usage of algorithms to be judged.

Critical response

Knuth was awarded the 1974

Turing Award The ACM A. M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) for contributions of lasting and major technical importance to computer science. It is generally recognized as the highest distinction in compu ...

"for his major contributions to the

analysis of algorithms In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other resources needed to execute them. Usually, this involves determining a function that re ...

�� and in particular for his contributions to the 'art of computer programming' through his well-known books in a continuous series by this title." ''

American Scientist __NOTOC__ ''American Scientist'' (informally abbreviated ''AmSci'') is an American bimonthly science and technology magazine published since 1913 by Sigma Xi, The Scientific Research Society. In the beginning of 2000s the headquarters was in New ...

'' has included this work among "100 or so Books that shaped a Century of Science", referring to the twentieth century, Covers of the third edition of Volume 1 quote

Bill Gates William Henry Gates III (born October 28, 1955) is an American business magnate and philanthropist. He is a co-founder of Microsoft, along with his late childhood friend Paul Allen. During his career at Microsoft, Gates held the positions ...

as saying, "If you think you're a really good programmer… read (Knuth's) ''Art of Computer Programming''… You should definitely send me a résumé if you can read the whole thing." ''

The New York Times ''The New York Times'' (''the Times'', ''NYT'', or the Gray Lady) is a daily newspaper based in New York City with a worldwide readership reported in 2020 to comprise a declining 840,000 paid print subscribers, and a growing 6 million paid ...

'' referred to it as "the profession's defining treatise".

Volumes

Completed

* Volume 1 – Fundamental Algorithms ** Chapter 1 – Basic concepts ** Chapter 2 – Information structures * Volume 2 – Seminumerical Algorithms ** Chapter 3 – Random numbers ** Chapter 4 –

Arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

* Volume 3 –

Sorting Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. # ordering: arranging items in a sequence ordered by some criterion; # categorizing: grouping items with similar pro ...

and Searching ** Chapter 5 –

** Chapter 6 – Searching * Volume 4A – Combinatorial Algorithms ** Chapter 7 – Combinatorial searching (part 1) * Volume 4B – Combinatorial Algorithms ** Chapter 7 – Combinatorial searching (part 2)

Planned

* Volume 4C, 4D, ... Combinatorial Algorithms (chapters 7 & 8 released in several subvolumes) ** Chapter 7 – Combinatorial searching (continued) ** Chapter 8 –

Recursion Recursion (adjective: ''recursive'') occurs when a thing is defined in terms of itself or of its type. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics ...

* Volume 5 – Syntactic Algorithms ** Chapter 9 – Lexical scanning (also includes

string search In computer science, string-searching algorithms, sometimes called string-matching algorithms, are an important class of string algorithms that try to find a place where one or several strings (also called patterns) are found within a larger string ...

and data compression) ** Chapter 10 –

Parsing Parsing, syntax analysis, or syntactic analysis is the process of analyzing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar. The term ''parsing'' comes from Lati ...

techniques * Volume 6 – The Theory of Context-Free Languages * Volume 7 –

Compiler In computing, a compiler is a computer program that translates computer code written in one programming language (the ''source'' language) into another language (the ''target'' language). The name "compiler" is primarily used for programs that ...

Techniques

Chapter outlines

Completed

Volume 1 – Fundamental Algorithms

* Chapter 1 – Basic concepts ** 1.1.

Algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...

s ** 1.2. Mathematical Preliminaries *** 1.2.1.

Mathematical Induction Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...

*** 1.2.2. Numbers, Powers, and

Logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...

s *** 1.2.3. Sums and Products *** 1.2.4. Integer Functions and Elementary

Number Theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777� ...

*** 1.2.5.

Permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

s and

Factorial In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times (n-1) \times (n-2) \t ...

s *** 1.2.6. Binomial Coefficients *** 1.2.7.

Harmonic Numbers In mathematics, the -th harmonic number is the sum of the reciprocals of the first natural numbers: H_n= 1+\frac+\frac+\cdots+\frac =\sum_^n \frac. Starting from , the sequence of harmonic numbers begins: 1, \frac, \frac, \frac, \frac, \do ...

*** 1.2.8. Fibonacci Numbers *** 1.2.9. Generating Functions *** 1.2.10. Analysis of an Algorithm *** 1.2.11. Asymptotic Representations **** 1.2.11.1. The O-notation **** 1.2.11.2. Euler's summation formula **** 1.2.11.3. Some asymptotic calculations ** 1.3

(

in the hardback copy but updated by fascicle 1) *** 1.3.1. Description of MMIX *** 1.3.2. The MMIX Assembly Language *** 1.3.3. Applications to

s ** 1.4. Some Fundamental Programming Techniques *** 1.4.1. Subroutines *** 1.4.2. Coroutines *** 1.4.3. Interpretive Routines **** 1.4.3.1. A MIX simulator **** 1.4.3.2. Trace routines *** 1.4.4. Input and Output *** 1.4.5. History and Bibliography * Chapter 2 – Information Structures ** 2.1. Introduction ** 2.2. Linear Lists *** 2.2.1. Stacks, Queues, and Deques *** 2.2.2. Sequential Allocation *** 2.2.3. Linked Allocation (

topological sorting In computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge ''uv'' from vertex ''u'' to vertex ''v'', ''u'' comes before ''v'' in the ordering. For ins ...

) *** 2.2.4. Circular Lists *** 2.2.5. Doubly Linked Lists *** 2.2.6. Arrays and Orthogonal Lists ** 2.3. Trees *** 2.3.1. Traversing

Binary Trees In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tr ...

*** 2.3.2. Binary Tree Representation of Trees *** 2.3.3. Other Representations of Trees *** 2.3.4. Basic Mathematical Properties of Trees **** 2.3.4.1. Free trees **** 2.3.4.2. Oriented trees **** 2.3.4.3. The "infinity lemma" **** 2.3.4.4. Enumeration of trees **** 2.3.4.5. Path length **** 2.3.4.6. History and bibliography *** 2.3.5. Lists and

Garbage Collection Waste collection is a part of the process of waste management. It is the transfer of solid waste from the point of use and disposal to the point of treatment or landfill. Waste collection also includes the curbside collection of recyclable m ...

** 2.4. Multilinked Structures ** 2.5. Dynamic Storage Allocation ** 2.6. History and Bibliography

Volume 2 – Seminumerical Algorithms

* Chapter 3 – Random Numbers ** 3.1. Introduction ** 3.2. Generating Uniform Random Numbers *** 3.2.1. The Linear Congruential Method **** 3.2.1.1. Choice of modulus **** 3.2.1.2. Choice of multiplier **** 3.2.1.3. Potency *** 3.2.2. Other Methods ** 3.3. Statistical Tests *** 3.3.1. General Test Procedures for Studying Random Data *** 3.3.2. Empirical Tests *** 3.3.3. Theoretical Tests *** 3.3.4. The Spectral Test ** 3.4. Other Types of Random Quantities *** 3.4.1. Numerical Distributions *** 3.4.2. Random Sampling and Shuffling ** 3.5. What Is a

Random Sequence The concept of a random sequence is essential in probability theory and statistics. The concept generally relies on the notion of a sequence of random variables and many statistical discussions begin with the words "let ''X''1,...,''Xn'' be independ ...

? ** 3.6. Summary * Chapter 4 – Arithmetic ** 4.1. Positional Number Systems ** 4.2.

Floating Point In computing, floating-point arithmetic (FP) is arithmetic that represents real numbers approximately, using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. For example, 12.345 can be ...

Arithmetic *** 4.2.1. Single-Precision Calculations *** 4.2.2. Accuracy of Floating Point Arithmetic *** 4.2.3. Double-Precision Calculations *** 4.2.4. Distribution of Floating Point Numbers ** 4.3. Multiple Precision Arithmetic *** 4.3.1. The Classical Algorithms *** 4.3.2. Modular Arithmetic *** 4.3.3. How Fast Can We Multiply? ** 4.4.

Radix In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is t ...

Conversion ** 4.5. Rational Arithmetic *** 4.5.1. Fractions *** 4.5.2. The Greatest Common Divisor *** 4.5.3. Analysis of Euclid's Algorithm *** 4.5.4. Factoring into Primes ** 4.6.

Polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An exa ...

Arithmetic *** 4.6.1. Division of Polynomials *** 4.6.2. Factorization of Polynomials *** 4.6.3. Evaluation of Powers (

addition-chain exponentiation In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. Using ''the form of'' the shortest addition chain, with multipl ...

) *** 4.6.4. Evaluation of Polynomials ** 4.7. Manipulation of

Power Series In mathematics, a power series (in one variable) is an infinite series of the form \sum_^\infty a_n \left(x - c\right)^n = a_0 + a_1 (x - c) + a_2 (x - c)^2 + \dots where ''an'' represents the coefficient of the ''n''th term and ''c'' is a const ...

Volume 3 – Sorting and Searching

* Chapter 5 –

** 5.1. Combinatorial Properties of

s *** 5.1.1. Inversions *** 5.1.2. Permutations of a Multiset *** 5.1.3. Runs *** 5.1.4. Tableaux and Involutions ** 5.2. Internal sorting *** 5.2.1. Sorting by Insertion *** 5.2.2. Sorting by Exchanging *** 5.2.3. Sorting by Selection *** 5.2.4. Sorting by Merging *** 5.2.5. Sorting by Distribution ** 5.3. Optimum Sorting *** 5.3.1. Minimum-Comparison Sorting *** 5.3.2. Minimum-Comparison Merging *** 5.3.3. Minimum-Comparison Selection *** 5.3.4. Networks for Sorting ** 5.4. External Sorting *** 5.4.1. Multiway Merging and Replacement Selection *** 5.4.2. The Polyphase Merge *** 5.4.3. The Cascade Merge *** 5.4.4. Reading Tape Backwards *** 5.4.5. The Oscillating Sort *** 5.4.6. Practical Considerations for Tape Merging *** 5.4.7. External Radix Sorting *** 5.4.8. Two-Tape Sorting *** 5.4.9. Disks and Drums ** 5.5. Summary, History, and Bibliography * Chapter 6 – Searching ** 6.1. Sequential Searching ** 6.2. Searching by Comparison of

Keys Key or The Key may refer to: Common meanings * Key (cryptography), a piece of information that controls the operation of a cryptography algorithm * Key (lock), device used to control access to places or facilities restricted by a lock * Key (map ...

*** 6.2.1. Searching an Ordered Table *** 6.2.2. Binary Tree Searching *** 6.2.3. Balanced Trees *** 6.2.4. Multiway Trees ** 6.3. Digital Searching ** 6.4. Hashing ** 6.5. Retrieval on Secondary Keys

Volume 4A – Combinatorial Algorithms, Part 1

* Chapter 7 – Combinatorial Searching ** 7.1.

Zeros and Ones ''Zeros and Ones'' is a 2021 American-Italian thriller film written and directed by Abel Ferrara and starring Ethan Hawke. It premiered at the 74th Locarno Film Festival in August 2021, and was released in limited theaters, on demand, and digit ...

*** 7.1.1.

Boolean Any kind of logic, function, expression, or theory based on the work of George Boole is considered Boolean. Related to this, "Boolean" may refer to: * Boolean data type, a form of data with only two possible values (usually "true" and "false" ...

Basics *** 7.1.2. Boolean Evaluation *** 7.1.3. Bitwise Tricks and Techniques *** 7.1.4.

Binary Decision Diagrams In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Un ...

** 7.2. Generating All Possibilities *** 7.2.1. Generating Basic Combinatorial Patterns **** 7.2.1.1. Generating all n-

tuple In mathematics, a tuple is a finite ordered list (sequence) of elements. An -tuple is a sequence (or ordered list) of elements, where is a non-negative integer. There is only one 0-tuple, referred to as ''the empty tuple''. An -tuple is defi ...

s **** 7.2.1.2. Generating all

permutation In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or proc ...

s **** 7.2.1.3. Generating all combinations **** 7.2.1.4. Generating all

partitions Partition may refer to: Computing Hardware * Disk partitioning, the division of a hard disk drive * Memory partition, a subdivision of a computer's memory, usually for use by a single job Software * Partition (database), the division of a ...

**** 7.2.1.5. Generating all set partitions **** 7.2.1.6. Generating all trees **** 7.2.1.7. History and further references

Volume 4B – Combinatorial Algorithms, Part 2

* Chapter 7 – Combinatorial Searching (continued) ** 7.2. Generating all possibilities (continued) *** 7.2.2. Backtrack programming **** 7.2.2.1.

Dancing links In computer science, dancing links (DLX) is a technique for adding and deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Knuth's Algorithm X for the exact ...

(includes discussion of

Exact cover In the mathematical field of combinatorics, given a collection of subsets of a set , an exact cover is a subcollection of such that each element in is contained in ''exactly one'' subset in . In other words, is a partition of consisting of s ...

) **** 7.2.2.2. Satisfiability

Planned

Volumes 4C, 4D, 4E, 4F – Combinatorial Algorithms

* Chapter 7 – Combinatorial Searching (continued) ** 7.2. Generating all possibilities (continued) *** 7.2.2. Backtrack programming (continued) **** 7.2.2.3. Constraint satisfaction **** 7.2.2.4. Hamiltonian paths and cycles **** 7.2.2.5. Cliques **** 7.2.2.6. Covers ( Vertex cover, Set cover problem,

Clique cover In graph theory, a clique cover or partition into cliques of a given undirected graph is a partition of the vertices into cliques, subsets of vertices within which every two vertices are adjacent. A minimum clique cover is a clique cover that use ...

) **** 7.2.2.7. Squares **** 7.2.2.8. A potpourri of puzzles (includes

Perfect digital invariant In number theory, a perfect digital invariant (PDI) is a number in a given number base (b) that is the sum of its own digits each raised to a given power (p). 0 F_ : \mathbb \rightarrow \mathbb is defined as: :F_(n) = \sum_^ d_i^p. where k = \lfloo ...

) **** 7.2.2.9. Estimating backtrack costs (chapter 6 of "Selected Papers on Analysis of Algorithms", and Fascicle 5, pp. 44−47, under the heading "Running time estimates") *** 7.2.3. Generating inequivalent patterns (includes discussion of Pólya enumeration theorem) (see "Techniques for Isomorph Rejection", chapter 4 of "Classification Algorithms for Codes and Designs" by Kaski and Östergård) ** 7.3. Shortest paths ** 7.4. Graph algorithms *** 7.4.1. Components and traversal **** 7.4.1.1.

Union-find algorithm In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set ...

s **** 7.4.1.2.

Depth-first search Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible alon ...

**** 7.4.1.3. Vertex and edge connectivity *** 7.4.2. Special classes of graphs *** 7.4.3. Expander graphs *** 7.4.4. Random graphs ** 7.5. Graphs and optimization *** 7.5.1. Bipartite matching (including maximum-cardinality matching,

Stable marriage problem In mathematics, economics, and computer science, the stable marriage problem (also stable matching problem or SMP) is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each elem ...

Mariages Stables
*** 7.5.2. The assignment problem *** 7.5.3. Network flows *** 7.5.4. Optimum subtrees *** 7.5.5. Optimum matching *** 7.5.6. Optimum orderings ** 7.6. Independence theory *** 7.6.1. Independence structures *** 7.6.2. Efficient matroid algorithms ** 7.7. Discrete

dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

(see also Transfer-matrix method) ** 7.8.

Branch-and-bound Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutio ...

techniques ** 7.9. Herculean tasks (aka

NP-hard In computational complexity theory, NP-hardness ( non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP". A simple example of an NP-hard pr ...

problems) ** 7.10. Near-optimization * Chapter 8 –

(chapter 22 of "Selected Papers on Analysis of Algorithms")

Volume 5 – Syntactic Algorithms

* Chapter 9 – Lexical scanning (includes also

and data compression) * Chapter 10 –

techniques

Volume 6 – The Theory of Context-free Languages

Volume 7 – Compiler Techniques

English editions

Current editions

These are the current editions in order by volume number: * ''The Art of Computer Programming, Volumes 1-4B Boxed Set''. (Reading, Massachusetts: Addison-Wesley, 2023), 3904pp. ** ''Volume 1: Fundamental Algorithms''. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xx+650pp. . Errata

(2011-01-08)

(2022, 49th printing run, printing). Addenda

(2011). ** ''Volume 2: Seminumerical Algorithms''. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. . Errata

(2011-01-08)

(2022, 45th printing). Addenda

(2011). ** ''Volume 3: Sorting and Searching''. Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout. . Errata

(2011-01-08)

(2022, 45th printing). Addenda

(2011). ** ''Volume 4A: Combinatorial Algorithms, Part 1''. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2011), xv+883pp. . Errata

(2011)

(2022, 22nd printing). ** ''Volume 4B: Combinatorial Algorithms, Part 2''. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2023), xviii+714pp. . Errata

(2023). * ''Volume 1, Fascicle 1: MMIX – A RISC Computer for the New Millennium''. (Addison-Wesley, 2005-02-14) . Errata

(2020-03-16) (will be in the fourth edition of volume 1)

Previous editions

Complete volumes

These volumes were superseded by newer editions and are in order by date. * ''Volume 1: Fundamental Algorithms''. First edition, 1968, xxi+634pp, . * ''Volume 2: Seminumerical Algorithms''. First edition, 1969, xi+624pp, . * ''Volume 3: Sorting and Searching''. First edition, 1973, xi+723pp+foldout, . Errata

* ''Volume 1: Fundamental Algorithms''. Second edition, 1973, xxi+634pp, . Errata

* ''Volume 2: Seminumerical Algorithms''. Second edition, 1981, xiii+ 688pp, . Errata

* ''The Art of Computer Programming, Volumes 1-3 Boxed Set''. Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), pp. * ''The Art of Computer Programming, Volumes 1-4A Boxed Set''. Third Edition (Reading, Massachusetts: Addison-Wesley, 2011), 3168pp.

Fascicles

Volume 4, fascicle (book), Fascicles 0–4 were revised and published as Volume 4A. * ''Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions''. (Addison-Wesley Professional, 2008-04-28) vi+240pp, . Errata

(2011-01-01). * ''Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams''. (Addison-Wesley Professional, 2009-03-27) viii+260pp, . Errata

(2011-01-01). * ''Volume 4, Fascicle 2: Generating All Tuples and Permutations''. (Addison-Wesley, 2005-02-14) v+127pp, . Errata

(2011-01-01). * ''Volume 4, Fascicle 3: Generating All Combinations and Partitions''. (Addison-Wesley, 2005-07-26) vi+150pp, . Errata

(2011-01-01). * ''Volume 4, Fascicle 4: Generating All Trees; History of Combinatorial Generation''. (Addison-Wesley, 2006-02-06) vi+120pp, . Errata

(2011-01-01). Volume 4, Fascicles 5–6 were revised and published as Volume 4B. * ''Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Backtracking; Dancing Links''. (Addison-Wesley, 2019-11-22) xiii+382pp, . Errata

(2020-03-27) * ''Volume 4, Fascicle 6: Satisfiability''. (Addison-Wesley, 2015-12-08) xiii+310pp, . Errata

(2020-03-26)

Pre-fascicles

* Pre-fascicle
0A0B
an
0C
were revised and published as Volume 4, fascicle 0. * Pre-fascicle
1A
an
1B
were revised and published as Volume 4, fascicle 1. * Pre-fascicle
2A
an
2B
were revised and published as Volume 4, fascicle 2. * Pre-fascicle
3A
an
3B
were revised and published as Volume 4, fascicle 3. * Pre-fascicle
4A
an
4B
were revised * and published as Volume 4, fascicle 4. * Pre-fascicle
5A5B
an
5C
were revised and published as Volume 4, fascicle 5. * Pre-fascicl
6A
was revised and published as Volume 4, fascicle 6. The remaining pre-fascicles contain draft material that is set to appear in future fascicles and volumes. *
Volume 4, Pre-fascicle 7A: Constraint Satisfaction
' *
Volume 4, Pre-fascicle 8A: Hamiltonian Paths and Cycles
' *
Volume 4, Pre-fascicle 8B: Cliques
' *
Volume 4, Pre-fascicle 9B: A Potpourri of Puzzles
' *
Volume 4, Pre-fascicle 9C: Estimating Backtrack Costs
' *
Volume 4, Pre-fascicle 12A: Components and Traversal(PDF Version)
' *
Volume 4, Pre-fascicle 14A: Bipartite Matching
' *
Volume 4, Pre-fascicle 16A: Introduction to Recursion
'

References

Notes Citations Sources * *

External links

Overview of topics
(Knuth's personal homepage)
Oral history interview with Donald E. Knuth
at Charles Babbage Institute, University of Minnesota, Minneapolis. Knuth discusses software patenting,

structured programming Structured programming is a programming paradigm aimed at improving the clarity, quality, and development time of a computer program by making extensive use of the structured control flow constructs of selection ( if/then/else) and repetition ( ...

, collaboration and his development of

TeX Tex may refer to: People and fictional characters * Tex (nickname), a list of people and fictional characters with the nickname * Joe Tex (1933–1982), stage name of American soul singer Joseph Arrington Jr. Entertainment * ''Tex'', the Italian ...

. The oral history discusses the writing of ''The Art of Computer Programming''.
"Robert W Floyd, In Memoriam", by Donald E. Knuth
- (on the influence of Bob Floyd)
''TAoCP'' and its Influence of Computer Science (Softpanorama)
{{DEFAULTSORT:Art Of Computer Programming, The 1968 non-fiction books 1969 non-fiction books 1973 non-fiction books 1981 non-fiction books 2011 non-fiction books Addison-Wesley books American non-fiction books Analysis of algorithms Books by Donald Knuth Computer arithmetic algorithms Computer programming books Computer science books English-language books Monographs

History

Assembly language in the book

Critical response

Volumes

Completed

Planned

Chapter outlines

Completed

Volume 1 – Fundamental Algorithms

Volume 2 – Seminumerical Algorithms

Volume 3 – Sorting and Searching

Volume 4A – Combinatorial Algorithms, Part 1

Volume 4B – Combinatorial Algorithms, Part 2

Planned

Volumes 4C, 4D, 4E, 4F – Combinatorial Algorithms

Volume 5 – Syntactic Algorithms

Volume 6 – The Theory of Context-free Languages

Volume 7 – Compiler Techniques

English editions

Current editions

Previous editions

Complete volumes

Fascicles

Pre-fascicles

See also

References

External links