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The Art of Computer Programming
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<h2 id="history">History</h2> <p>After winning a <a href="/facts/Regeneron_Science_Talent_Search/g8CpSflC">Westinghouse Talent Search</a> scholarship, Knuth enrolled at the Case Institute of Technology (now <a href="/facts/Case_Western_Reserve_University/S0xlUbTM">Case Western Reserve University</a>), where his performance was so outstanding that the faculty voted to award him a <a href="/facts/Master_of_Science/5xKwvXjm">master of science</a> upon his completion of the <a href="/facts/Bachelor%2527s_degree/s739u69z">bachelor's degree</a>. During his summer vacations, Knuth was hired by the <a href="/facts/Burroughs_Corporation/NAEwIvpU">Burroughs Corporation</a> to write <a href="/facts/Compiler/WNfCDFJe">compilers</a>, earning more in his summer months than full professors did for an entire year.<a class="footnote-ref" id="fnref:7" href="#fn:7"><sup>7</sup></a> Such exploits made Knuth a topic of discussion among the mathematics department, which included <a href="/facts/Richard_S._Varga/hJhVIvoY">Richard S. Varga</a>. </p><p>In January 1962, when he was a graduate student in the mathematics department at Caltech, Knuth was approached by <a href="/facts/Addison-Wesley/A7UFATEG">Addison-Wesley</a> 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 <a href="/facts/Fortran/m1KqjcMU">FORTRAN</a> compiler for <a href="/facts/UNIVAC/FhJlhtva">UNIVAC</a>, considering that he had "sold my soul to the devil" to develop a FORTRAN compiler<a class="footnote-ref" id="fnref:8" href="#fn:8"><sup>8</sup></a>: 15 after <a href="/facts/ALGOL/mw03yQdn">ALGOL</a> developments with Burroughs. He remained as a consultant to Burroughs over the period 1960 to 1968 while writing Volume 1 "Fundamental Algorithms". </p><p>During this time, he also developed a mathematical analysis of <a href="/facts/Linear_probing/wCvUHGF3">linear probing</a>, 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 3000 hand-written pages.<a class="footnote-ref" id="fnref:9" href="#fn:9"><sup>9</sup></a> He had assumed that about five hand-written pages would translate into one printed page, but his publisher said instead that about 1+1⁄2 hand-written pages translated to one printed page. This meant he had approximately 2000 printed pages of material, which closely matches the size of the first three published volumes. </p><p>The first volume of "The Art of Computer Programming", "Fundamental Algorithms", took five years to complete between 1963 and 1968 while working at both Caltech and Burroughs. </p><p>Knuth's dedication in Volume 1 reads: </p> <blockquote><p>This series of books is affectionately dedicatedto the <a href="/facts/IBM_650/l5mCAMIF">Type 650 computer</a> once installed at<a href="/facts/Case_Institute_of_Technology/S0xlUbTM">Case Institute of Technology</a>,in remembrance of many pleasant evenings.<a class="footnote-ref" id="fnref:10" href="#fn:10"><sup>10</sup></a></p></blockquote> <p>In the preface, he thanks first his wife Jill, then Burroughs for the use of B220 and B5500 computers in testing most of the programs, and Caltech, the National Science Foundation, and the Office of Naval Research.<a class="footnote-ref" id="fnref:11" href="#fn:11"><sup>11</sup></a>: xii </p><p>Section 2.5 of "Fundamental Algorithms" is on <a href="/facts/Dynamic_memory_allocation/vthLkUpz">Dynamic Storage Allocation</a>. Parts of this are used in the Burroughs approach to memory management. Knuth claims credit for “The “boundary-tag” method, introduced in Section 2.5, was designed by the author in 1962 for use in a control program for the B5000 computer.”<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a>: 460 </p><p>Knuth received support from Richard S. Varga, who was the scientific adviser to the publisher. Varga was visiting <a href="/facts/Olga_Taussky-Todd/0VkhPMcP">Olga Taussky-Todd</a> and <a href="/facts/John_Todd_(computer_scientist)/Lbsl9r7s">John Todd</a> at <a href="/facts/Caltech/3FPcp7BL">Caltech</a>. 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.<a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> 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. </p><p>In 1976, Knuth prepared a second edition of Volume 2, requiring it to be <a href="/facts/Typesetting/CsKmfY0t">typeset</a> again, but the style of type used in the first edition (called <a href="/facts/Hot_metal_typesetting/1VA72CVR">hot type</a>) was no longer available. In 1977, he decided to spend some time creating something more suitable. Eight years later, he returned with <a href="/facts/TeX/8t3cCBqk">TEX</a>, which is currently used for all volumes. </p><p>Another characteristic of the volumes is the variation in the difficulty of the exercises including a numerical rating varying from 0 to 50, where 0 is trivial, and 50 is an open question in contemporary research. </p> <h2 id="bounty-for-finding-errors">Bounty for finding errors</h2> <p>The offer of a so-called <a href="/facts/Knuth_reward_check/kqubcFGm">Knuth reward check</a> worth "one hexadecimal dollar" (100<a href="/facts/Hexadecimal/02ohQW22">HEX</a> <a href="/facts/Hexadecimal/02ohQW22">base 16</a> cents, in <a href="/facts/Decimal/7omfVNIM">decimal</a>, 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. </p> <h2 id="assembly-language-in-the-book">Assembly language in the book</h2> <p>All examples in the books use a hypothetical language called "<a href="/facts/MIX_(abstract_machine)/C7JqgIMI">MIX</a> assembly language" (MIXAL), which runs on "a mythical computer called MIX". Currently,[<i>when?</i>] the MIX computer is being replaced by the <a href="/facts/MMIX/ttL2sAbM">MMIX</a> computer, which is a <a href="/facts/RISC/aQbGM62p">RISC</a> version. The conversion from MIX to MMIX was a large ongoing project for which Knuth solicited volunteers for help. Software such as GNU MDK<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> exists to provide <a href="/facts/Emulator/FMHE8qDj">emulation</a> of the MIX architecture. Knuth considers the use of <a href="/facts/Assembly_language/7XuV0cla">assembly language</a> necessary for the speed and memory usage of algorithms to be judged. </p><p>MIX was much like any computer then in existence, but nicer. The name ‘MIX’ is 1009 in Roman numerals and this is given by a formula involving series numbers of several computers of the time: (360 + 650 + 709 + U3 + SS80 + 1107 + 1604 + G2- + B220 + S2000 + 920 + 601 + H800 + PDP-4 + 11)/16 = 1009 or MIX. The name MMIX is 2009 in Roman numerals and Knuth claims MMIX is even nicer than MIX. </p> <h2 id="critical-response">Critical response</h2> <p>Knuth was awarded the 1974 <a href="/facts/Turing_Award/HbEEp0GF">Turing Award</a> "for his major contributions to the <a href="/facts/Analysis_of_algorithms/pStoBgBn">analysis of algorithms</a> […], and in particular for his contributions to the 'art of computer programming' through his well-known books in a continuous series by this title."<a class="footnote-ref" id="fnref:15" href="#fn:15"><sup>15</sup></a> <i><a href="/facts/American_Scientist/M40emvcm">American Scientist</a></i> has included this work among "100 or so Books that shaped a Century of Science", referring to the twentieth century.<a class="footnote-ref" id="fnref:16" href="#fn:16"><sup>16</sup></a> Covers of the third edition of Volume 1 quote <a href="/facts/Bill_Gates/z16t4m7s">Bill Gates</a> as saying, "If you think you're a really good programmer… read (Knuth's) <i>Art of Computer Programming</i>… You should definitely send me a résumé if you can read the whole thing."<a class="footnote-ref" id="fnref:17" href="#fn:17"><sup>17</sup></a> <i><a href="/facts/The_New_York_Times/T9marWVX">The New York Times</a></i> referred to it as "the profession's defining treatise".<a class="footnote-ref" id="fnref:18" href="#fn:18"><sup>18</sup></a> </p> <h2 id="volumes">Volumes</h2> <h3>Completed</h3> <ul><li>Volume 1 – Fundamental algorithms <ul><li>Chapter 1 – Basic concepts</li> <li>Chapter 2 – Information <a href="/facts/Data_structure/yNsNvL1I">structures</a></li></ul></li> <li>Volume 2 – Seminumerical algorithms <ul><li>Chapter 3 – <a href="/facts/Statistical_randomness/Ns0bkleV">Random numbers</a></li> <li>Chapter 4 – <a href="/facts/Arithmetic/hvHwkbMV">Arithmetic</a></li></ul></li> <li>Volume 3 – <a href="/facts/Sorting_algorithm/PwHpj1Gs">Sorting</a> and <a href="/facts/Search_algorithm/eJuw0nyz">searching</a> <ul><li>Chapter 5 – <a href="/facts/Sorting_algorithm/PwHpj1Gs">Sorting</a></li> <li>Chapter 6 – <a href="/facts/Search_algorithm/eJuw0nyz">Searching</a></li></ul></li> <li>Volume 4A – <a href="/facts/Combinatorics/k14xUoKT">Combinatorial</a> algorithms <ul><li>Chapter 7 – Combinatorial searching (part 1)</li></ul></li> <li>Volume 4B – <a href="/facts/Combinatorics/k14xUoKT">Combinatorial</a> algorithms <ul><li>Chapter 7 – Combinatorial searching (part 2)</li></ul></li></ul> <h3>Planned</h3> <ul><li>Volume 4C, 4D, ... Combinatorial algorithms (chapters 7 & 8 released in several subvolumes) <ul><li>Chapter 7 – Combinatorial searching (continued)</li> <li>Chapter 8 – <a href="/facts/Recursion/CxSKxJoW">Recursion</a></li></ul></li> <li>Volume 5 – Syntactic algorithms <ul><li>Chapter 9 – <a href="/facts/Lexical_analysis/T1JYWpIf">Lexical scanning</a> (also includes <a href="/facts/String_searching_algorithm/RCvwDRle">string search</a> and <a href="/facts/Data_compression/gMFuY4FT">data compression</a>)</li> <li>Chapter 10 – <a href="/facts/Parsing/nRKB01S3">Parsing</a> techniques</li></ul></li> <li>Volume 6 – The Theory of <a href="/facts/Context-free_language/sHDxB5So">context-free languages</a> <ul><li>Chapter 11 – <a href="/facts/Mathematical_linguistics/XmegJ6LC">Mathematical linguistics</a></li></ul></li> <li>Volume 7 – <a href="/facts/Compiler/WNfCDFJe">Compiler</a> techniques <ul><li>Chapter 12 – Programming language translation</li></ul></li></ul> <h2 id="chapter-outlines">Chapter outlines</h2> <h3>Completed</h3> <h4>Volume 1 – Fundamental algorithms</h4> <ul><li>Chapter 1 – Basic concepts <ul><li>1.1. <a href="/facts/Algorithm/fnl5NmRt">Algorithms</a></li> <li>1.2. Mathematical preliminaries <ul><li>1.2.1. <a href="/facts/Mathematical_induction/KxAPqNrH">Mathematical induction</a></li> <li>1.2.2. Numbers, powers, and <a href="/facts/Logarithm/QeXaV97q">logarithms</a></li> <li>1.2.3. Sums and products</li> <li>1.2.4. Integer functions and elementary <a href="/facts/Number_theory/zhoa7zrc">number theory</a></li> <li>1.2.5. <a href="/facts/Permutation/JSw9ukmv">Permutations</a> and <a href="/facts/Factorial/kkfy1Bwe">factorials</a></li> <li>1.2.6. <a href="/facts/Binomial_coefficient/Tsx7eY5h">Binomial coefficients</a></li> <li>1.2.7. <a href="/facts/Harmonic_number/1b7v0hVn">Harmonic numbers</a></li> <li>1.2.8. <a href="/facts/Fibonacci_number/mqxpAUQD">Fibonacci numbers</a></li> <li>1.2.9. <a href="/facts/Generating_function/K7UVjnjL">Generating functions</a></li> <li>1.2.10. Analysis of an algorithm</li> <li>1.2.11. <a href="/facts/Asymptotic_analysis/kt87qLpu">Asymptotic representations</a> <ul><li>1.2.11.1. The <a href="/facts/Big_O_notation/weFFjSWg">O-notation</a></li> <li>1.2.11.2. <a href="/facts/Euler%2527s_summation_formula/mN6uNCzN">Euler's summation formula</a></li> <li>1.2.11.3. Some asymptotic calculations</li></ul></li></ul></li> <li>1.3 <a href="/facts/MIX_(abstract_machine)/C7JqgIMI">MIX</a> (Updated with <a href="/facts/MMIX/ttL2sAbM">MMIX</a><a class="footnote-ref" id="fnref:19" href="#fn:19"><sup>19</sup></a> in Volume 1 fascicle 1) <ul><li>1.3.1. Description of MIX</li> <li>1.3.2. The MIX assembly language</li> <li>1.3.3. Applications to <a href="/facts/Permutation/JSw9ukmv">permutations</a></li></ul></li> <li>1.4. Some fundamental programming techniques <ul><li>1.4.1. <a href="/facts/Function_(computer_programming)/9vFJrg0A">Subroutines</a></li> <li>1.4.2. <a href="/facts/Coroutine/hGCtXsAQ">Coroutines</a></li> <li>1.4.3. Interpretive routines <ul><li>1.4.3.1. A MIX simulator</li> <li>1.4.3.2. Trace routines</li></ul></li> <li>1.4.4. <a href="/facts/Input%2foutput/WQTE8Jas">Input and output</a></li> <li>1.4.5. History and bibliography</li></ul></li></ul></li> <li>Chapter 2 – Information structures <ul><li>2.1. Introduction</li> <li>2.2. <a href="/facts/List_(abstract_data_type)/9tzhAH6M">Linear lists</a> <ul><li>2.2.1. <a href="/facts/Stack_(abstract_data_type)/bj7l94v1">Stacks</a>, <a href="/facts/Queue_(abstract_data_type)/hVPjPXus">queues</a>, and <a href="/facts/Double-ended_queue/pQboJcly">deques</a></li> <li>2.2.2. Sequential allocation</li> <li>2.2.3. Linked allocation (<a href="/facts/Topological_sorting/VY7gNtYA">topological sorting</a>)</li> <li>2.2.4. Circular lists</li> <li>2.2.5. Doubly linked lists</li> <li>2.2.6. <a href="/facts/Array_(data_structure)/BKGvF8AM">Arrays</a> and orthogonal lists</li></ul></li> <li>2.3. <a href="/facts/Tree_(data_structure)/RcXz9noF">Trees</a> <ul><li>2.3.1. Traversing <a href="/facts/Binary_tree/TDV7GMpu">binary trees</a></li> <li>2.3.2. Binary tree representation of trees</li> <li>2.3.3. Other representations of trees</li> <li>2.3.4. Basic mathematical properties of trees <ul><li>2.3.4.1. Free trees</li> <li>2.3.4.2. <a href="/facts/Polytree/pcJa4qeS">Oriented trees</a></li> <li>2.3.4.3. <a href="/facts/K%25C5%2591nig%2527s_lemma/eCU93PN9">The "infinity lemma"</a></li> <li>2.3.4.4. Enumeration of trees</li> <li>2.3.4.5. Path length</li> <li>2.3.4.6. History and bibliography</li></ul></li> <li>2.3.5. Lists and <a href="/facts/Garbage_collection_(computer_science)/j2vlIu7g">garbage collection</a></li></ul></li> <li>2.4. Multilinked structures</li> <li>2.5. <a href="/facts/Dynamic_memory_allocation/vthLkUpz">Dynamic storage allocation</a></li> <li>2.6. History and bibliography</li></ul></li></ul> <h4>Volume 2 – Seminumerical algorithms</h4> <ul><li>Chapter 3 – <a href="/facts/Random_number/lSGGA5gW">Random numbers</a> <ul><li>3.1. Introduction</li> <li>3.2. <a href="/facts/Pseudo-random_number_generator/sIrCxIBq">Generating uniform random numbers</a> <ul><li>3.2.1. The <a href="/facts/Linear_congruential_generator/E4PyJQ5U">linear congruential</a> method <ul><li>3.2.1.1. Choice of modulus</li> <li>3.2.1.2. Choice of multiplier</li> <li>3.2.1.3. Potency</li></ul></li> <li>3.2.2. Other methods</li></ul></li> <li>3.3. Statistical tests <ul><li>3.3.1. General test procedures for studying random data</li> <li>3.3.2. Empirical tests</li> <li>3.3.3. Theoretical tests</li> <li>3.3.4. The spectral test</li></ul></li> <li>3.4. <a href="/facts/Pseudo-random_number_sampling/xIkyQJqu">Other types of random quantities</a> <ul><li>3.4.1. Numerical distributions</li> <li>3.4.2. Random sampling and <a href="/facts/Fisher%25E2%2580%2593Yates_shuffle/fIkuVG2X">shuffling</a></li></ul></li> <li>3.5. What Is a <a href="/facts/Random_Sequence/z2uHfvK4">random sequence</a>?</li> <li>3.6. Summary</li></ul></li> <li>Chapter 4 – Arithmetic <ul><li>4.1. <a href="/facts/Positional_notation/31DECoN4">Positional number systems</a></li> <li>4.2. <a href="/facts/Floating_point/eIckahxe">Floating point</a> arithmetic <ul><li>4.2.1. Single-precision calculations</li> <li>4.2.2. Accuracy of floating point arithmetic</li> <li>4.2.3. Double-precision calculations</li> <li>4.2.4. Distribution of floating point numbers</li></ul></li> <li>4.3. <a href="/facts/Arbitrary-precision_arithmetic/cXxc8yB2">Multiple precision arithmetic</a> <ul><li>4.3.1. The classical algorithms</li> <li>4.3.2. Modular arithmetic</li> <li>4.3.3. How fast can we multiply?</li></ul></li> <li>4.4. <a href="/facts/Radix/J5RGWRJF">Radix</a> conversion</li> <li>4.5. <a href="/facts/Rational_number/VJQmyY05">Rational</a> arithmetic <ul><li>4.5.1. Fractions</li> <li>4.5.2. The greatest common divisor</li> <li>4.5.3. Analysis of <a href="/facts/Euclidean_algorithm/wApql29c">Euclid's algorithm</a></li> <li>4.5.4. Factoring into primes</li></ul></li> <li>4.6. <a href="/facts/Polynomial/Lzak8VVx">Polynomial</a> arithmetic <ul><li>4.6.1. Division of polynomials</li> <li>4.6.2. Factorization of polynomials</li> <li>4.6.3. Evaluation of powers (<a href="/facts/Addition-chain_exponentiation/JkGjVadw">addition-chain exponentiation</a>)</li> <li>4.6.4. Evaluation of polynomials</li></ul></li> <li>4.7. Manipulation of <a href="/facts/Power_Series/vYh6sTps">power series</a></li></ul></li></ul> <h4>Volume 3 – Sorting and searching</h4> <ul><li>Chapter 5 – <a href="/facts/Sorting_algorithm/PwHpj1Gs">Sorting</a> <ul><li>5.1. Combinatorial properties of <a href="/facts/Permutation/JSw9ukmv">permutations</a> <ul><li>5.1.1. Inversions</li> <li>5.1.2. Permutations of a multiset</li> <li>5.1.3. Runs</li> <li>5.1.4. Tableaux and involutions</li></ul></li> <li>5.2. <a href="/facts/Internal_sort/Da4vCuUA">Internal sorting</a> <ul><li>5.2.1. Sorting by insertion</li> <li>5.2.2. Sorting by exchanging</li> <li>5.2.3. Sorting by selection</li> <li>5.2.4. Sorting by merging</li> <li>5.2.5. Sorting by distribution</li></ul></li> <li>5.3. Optimum sorting <ul><li>5.3.1. Minimum-comparison sorting</li> <li>5.3.2. Minimum-comparison merging</li> <li>5.3.3. Minimum-comparison selection</li> <li>5.3.4. Networks for sorting</li></ul></li> <li>5.4. <a href="/facts/External_Sorting/WaCt6XFC">External sorting</a> <ul><li>5.4.1. Multiway merging and replacement selection</li> <li>5.4.2. The polyphase merge</li> <li>5.4.3. The cascade merge</li> <li>5.4.4. Reading tape backwards</li> <li>5.4.5. The oscillating sort</li> <li>5.4.6. Practical considerations for tape merging</li> <li>5.4.7. External radix sorting</li> <li>5.4.8. Two-tape sorting</li> <li>5.4.9. Disks and drums</li></ul></li> <li>5.5. Summary, history, and bibliography</li></ul></li> <li>Chapter 6 – <a href="/facts/Search_algorithm/eJuw0nyz">Searching</a> <ul><li>6.1. Sequential searching</li> <li>6.2. Searching by comparison of <a href="/facts/Unique_key/NKGBxUHR">keys</a> <ul><li>6.2.1. Searching an ordered table</li> <li>6.2.2. Binary tree searching</li> <li>6.2.3. Balanced trees</li> <li>6.2.4. Multiway trees</li></ul></li> <li>6.3. Digital searching</li> <li>6.4. <a href="/facts/Hash_table/Ht4ptDPF">Hashing</a></li> <li>6.5. Retrieval on secondary keys</li></ul></li></ul> <h4>Volume 4A – Combinatorial algorithms, Part 1</h4> <ul><li>Chapter 7 – Combinatorial searching <ul><li>7.1. <a href="/facts/Binary_numeral_system/a6JDSRPs">Zeros and ones</a> <ul><li>7.1.1. <a href="/facts/Two-element_Boolean_algebra/8nIWUpwd">Boolean</a> basics</li> <li>7.1.2. Boolean evaluation</li> <li>7.1.3. <a href="/facts/Bitwise_operation/0gkqnUda">Bitwise</a> tricks and techniques</li> <li>7.1.4. <a href="/facts/Binary_decision_diagram/977o5E7L">Binary decision diagrams</a></li></ul></li> <li>7.2. Generating all possibilities <ul><li>7.2.1. Generating basic combinatorial patterns <ul><li>7.2.1.1. Generating all <i>n</i>-<a href="/facts/Tuple/BI1HIxL8">tuples</a></li> <li>7.2.1.2. Generating all <a href="/facts/Permutation/JSw9ukmv">permutations</a></li> <li>7.2.1.3. Generating all <a href="/facts/Combination/nmvrhMm1">combinations</a></li> <li>7.2.1.4. Generating all <a href="/facts/Integer_partition/LtyXWqwH">integer partitions</a></li> <li>7.2.1.5. Generating all <a href="/facts/Partition_of_a_set/VeP9g8CA">set partitions</a></li> <li>7.2.1.6. Generating all <a href="/facts/Tree_(graph_theory)/TCWk4Joy">trees</a></li> <li>7.2.1.7. History and further references</li></ul></li></ul></li></ul></li></ul> <h4>Volume 4B – Combinatorial algorithms, Part 2</h4> <ul><li>Chapter 7 – Combinatorial searching (continued) <ul><li>7.2. Generating all possibilities (continued) <ul><li>7.2.2. <a href="/facts/Backtracking/Jm9vDUk8">Backtrack programming</a> <ul><li>7.2.2.1. <a href="/facts/Dancing_links/WpaSJyuV">Dancing links</a> (includes discussion of <a href="/facts/Exact_cover/C7QcbDcN">exact cover</a>)</li> <li>7.2.2.2. <a href="/facts/Satisfiability/NkmQFgHB">Satisfiability</a></li></ul></li></ul></li></ul></li></ul> <h3>Planned</h3> <h4>Volumes 4C, 4D, 4E, 4F – Combinatorial algorithms</h4> <p>Source: <a class="footnote-ref" id="fnref:20" href="#fn:20"><sup>20</sup></a> </p> <ul><li>Chapter 7 – Combinatorial searching (continued) <ul><li>7.2. Generating all possibilities (continued) <ul><li>7.2.2. <a href="/facts/Backtracking/Jm9vDUk8">Backtrack programming</a> (continued) <ul><li>7.2.2.3. <a href="/facts/Constraint_Satisfaction_Problem/oKCeIV2L">Constraint satisfaction</a> (released as Fascicle 7)<a class="footnote-ref" id="fnref:21" href="#fn:21"><sup>21</sup></a></li> <li>7.2.2.4. <a href="/facts/Hamiltonian_path_problem/heMgdfpa">Hamiltonian paths</a> and cycles (released as <i><a href="https://cs.stanford.edu/~knuth/fasc8a.ps.gz">Pre-fascicle 8A</a></i>)</li> <li>7.2.2.5. <a href="/facts/Clique_problem/cVVBNP08">Cliques</a> (released as <i><a href="https://cs.stanford.edu/~knuth/fasc8b.ps.gz">Pre-fascicle 8B</a></i>)</li> <li>7.2.2.6. Covers (<a href="/facts/Vertex_cover/WK86bJvf">vertex cover</a>, <a href="/facts/Set_cover_problem/MVzyBYs1">set cover problem</a>, <a href="/facts/Exact_cover/C7QcbDcN">exact cover</a>, <a href="/facts/Clique_cover/tXT9GSVq">clique cover</a>)</li> <li>7.2.2.7. Squares</li> <li>7.2.2.8. A potpourri of puzzles (includes <a href="/facts/Perfect_digital_invariant/nXpHyK8d">perfect digital invariant</a>) (released as <i><a href="https://cs.stanford.edu/~knuth/fasc9b.ps.gz">Pre-fascicle 9B</a></i>)</li> <li>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")(released as <i><a href="https://cs.stanford.edu/~knuth/fasc9c.ps.gz">Pre-fascicle 9C</a></i>)</li></ul></li> <li>7.2.3. Generating inequivalent patterns (includes discussion of <a href="/facts/P%25C3%25B3lya_enumeration_theorem/EBbxaxkz">Pólya enumeration theorem</a>) (see "Techniques for Isomorph Rejection", chapter 4 of "Classification Algorithms for Codes and Designs" by Kaski and Östergård)</li></ul></li> <li>7.3. <a href="/facts/Shortest_path_problem/g4nsrswr">Shortest paths</a></li> <li>7.4. <a href="/facts/Graph_algorithms/g3uenNkc">Graph algorithms</a> <ul><li>7.4.1. Components and traversal <ul><li>7.4.1.1. <a href="/facts/Union-find_algorithm/QnFQNedE">Union-find algorithms</a></li> <li>7.4.1.2. <a href="/facts/Depth-first_search/luxJKVph">Depth-first search</a></li> <li>7.4.1.3. Vertex and edge connectivity</li></ul></li> <li>7.4.2. Special classes of graphs</li> <li>7.4.3. <a href="/facts/Expander_graph/21stncb0">Expander graphs</a></li> <li>7.4.4. <a href="/facts/Random_graph/gfQhq1Sz">Random graphs</a></li></ul></li> <li>7.5. Graphs and optimization <ul><li>7.5.1. Bipartite matching (including <a href="/facts/Maximum_cardinality_matching/oKaChmBt">maximum-cardinality matching</a>, <a href="/facts/Stable_marriage_problem/tzNRpF1f">stable marriage problem</a>, <a href="https://cs.stanford.edu/~knuth/ms.html">mariages stables</a>)(released as <i><a href="https://cs.stanford.edu/~knuth/fasc14a.ps.gz">Pre-fascicle 14A</a></i>)</li> <li>7.5.2. <a href="/facts/Assignment_problem/dIMpM0aW">The assignment problem</a></li> <li>7.5.3. <a href="/facts/Network_flow_problem/Tap21Rmw">Network flows</a></li> <li>7.5.4. Optimum subtrees</li> <li>7.5.5. Optimum matching</li> <li>7.5.6. Optimum orderings</li></ul></li> <li>7.6. Independence theory <ul><li>7.6.1. Independence structures</li> <li>7.6.2. Efficient <a href="/facts/Matroid/5bLcGlRF">matroid</a> algorithms</li></ul></li> <li>7.7. Discrete <a href="/facts/Dynamic_programming/CLcabtmk">dynamic programming</a> (see also <a href="/facts/Transfer-matrix_method_(statistical_mechanics)/gjkfQFdB">transfer-matrix method</a>)</li> <li>7.8. <a href="/facts/Branch-and-bound/mhALtav7">Branch-and-bound</a> techniques</li> <li>7.9. Herculean tasks (aka <a href="/facts/NP-hard/mQeNPv4R">NP-hard</a> problems)</li> <li>7.10. <a href="/facts/Approximation_algorithm/BWlf7M32">Near-optimization</a></li></ul></li> <li>Chapter 8 – <a href="/facts/Recursion/CxSKxJoW">Recursion</a> (chapter 22 of "Selected Papers on Analysis of Algorithms")</li></ul> <h4>Volume 5 – Syntactic algorithms</h4> <ul><li>Chapter 9 – <a href="/facts/Lexical_analysis/T1JYWpIf">Lexical scanning</a> (includes also <a href="/facts/Knuth%25E2%2580%2593Morris%25E2%2580%2593Pratt_algorithm/A4uM3D8e">string search</a> and data compression)</li> <li>Chapter 10 – <a href="/facts/Parsing/nRKB01S3">Parsing</a> techniques</li></ul> <h4>Volume 6 – The theory of context-free languages<a class="footnote-ref" id="fnref:22" href="#fn:22"><sup>22</sup></a></h4> <ul><li>Chapter 11 – <a href="/facts/Mathematical_linguistics/XmegJ6LC">Mathematical linguistics</a><a class="footnote-ref" id="fnref:23" href="#fn:23"><sup>23</sup></a></li></ul> <h4>Volume 7 – Compiler techniques</h4> <ul><li>Chapter 12 – <a href="/facts/Programming_language_translation/D3TIzmrI">Programming language translation</a><a class="footnote-ref" id="fnref:24" href="#fn:24"><sup>24</sup></a></li></ul> <h2 id="english-editions">English editions</h2> <h3>Current editions</h3> <p>These are the current editions in order by volume number: </p> <ul><li><i>The Art of Computer Programming, Volumes 1-4B Boxed Set</i>. (Reading, Massachusetts: Addison-Wesley, 2023), 3904pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-13-793510-9, 0-13-793510-2 <ul><li><i>Volume 1: Fundamental Algorithms</i>. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xx+650pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-89683-1, 0-201-89683-4. Errata: <a href="https://cs.stanford.edu/~knuth/all1-pre.ps.gz">[1]</a> (from 2011-01-08), <a href="https://cs.stanford.edu/~knuth/all1.ps.gz">[2]</a> (from 2022, 49th <a href="/facts/Printing_run/dU0Rmxf1">printing</a>). Addenda: <a href="https://cs.stanford.edu/~knuth/1-appc.ps.gz">[3]</a> (2011).</li> <li><i>Volume 2: Seminumerical Algorithms</i>. Third Edition (Reading, Massachusetts: Addison-Wesley, 1997), xiv+762pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-89684-8, 0-201-89684-2. Errata: <a href="https://cs.stanford.edu/~knuth/all2-pre.ps.gz">[4]</a> (from 2011-01-08), <a href="https://cs.stanford.edu/~knuth/all2.ps.gz">[5]</a> (from 2022, 45th printing). Addenda: <a href="https://cs.stanford.edu/~knuth/2-appc.ps.gz">[6]</a> (2011).</li> <li><i>Volume 3: Sorting and Searching</i>. Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), xiv+780pp.+foldout. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-89685-5, 0-201-89685-0. Errata: <a href="https://cs.stanford.edu/~knuth/all3-pre.ps.gz">[7]</a> (from 2011-01-08), <a href="https://cs.stanford.edu/~knuth/all3.ps.gz">[8]</a> (from 2022, 45th printing). Addenda: <a href="https://cs.stanford.edu/~knuth/3-appc.ps.gz">[9]</a> (2011).</li> <li><i>Volume 4A: Combinatorial Algorithms, Part 1</i>. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2011, 24th printing), xv+883pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-03804-0, 0-201-03804-8. Errata: <a href="https://cs.stanford.edu/~knuth/all4a-pre.ps.gz">[10]</a> (from 2011), <a href="https://cs.stanford.edu/~knuth/all4a.ps.gz">[11]</a> (from 2022, 20th printing).</li> <li><i>Volume 4B: Combinatorial Algorithms, Part 2</i>. First Edition (Upper Saddle River, New Jersey: Addison-Wesley, 2023, 2nd printing), xviii+714pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-03806-4, 0-201-03806-4. Errata: <a href="https://cs.stanford.edu/~knuth/all4b.ps.gz">[12]</a> (from 2023, 1st printing).</li></ul></li> <li><i>Volume 1, Fascicle 1: MMIX – A RISC Computer for the New Millennium</i>. (Addison-Wesley, 2005-02-14), 144pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-85392-2. Errata: <a href="https://cs.stanford.edu/~knuth/all1f1.ps.gz">[13]</a> (from 2005, 1st printing) (will be in the fourth edition of volume 1)</li> <li><i>The MMIX Supplement</i> by Martin Ruckert. (Addison-Wesley), 193pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-13-399231-4. A conversion of the MIX problems/programs in volumes 1, 2 & 3 to MMIX.</li> <li><i>Volume 4, Fascicle 7: Constraint Satisfaction</i>. (Addison-Wesley, 2025-02-05), xiv+281pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-13-532824-8.</li></ul> <h3>Previous editions</h3> <h4>Complete volumes</h4> <p>These volumes were superseded by newer editions and are in order by date. </p> <ul><li><i>Volume 1: Fundamental Algorithms</i>. First edition, 1968, xxi+634pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-03801-3.<a class="footnote-ref" id="fnref:25" href="#fn:25"><sup>25</sup></a></li> <li><i>Volume 2: Seminumerical Algorithms</i>. First edition, 1969, xi+624pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-03802-1.<a class="footnote-ref" id="fnref:26" href="#fn:26"><sup>26</sup></a></li> <li><i>Volume 3: Sorting and Searching</i>. First edition, 1973, xi+723pp+foldout, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-03803-X. Errata: <a href="https://cs.stanford.edu/~knuth/err3-1e.ps.gz">[14]</a>.</li> <li><i>Volume 1: Fundamental Algorithms</i>. Second edition, 1973, xxi+634pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-03809-9. Errata: <a href="https://cs.stanford.edu/~knuth/err1-2e.ps.gz">[15]</a>.</li> <li><i>Volume 2: Seminumerical Algorithms</i>. Second edition, 1981, xiii+ 688pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-03822-6. Errata: <a href="https://cs.stanford.edu/~knuth/err2-2e.ps.gz">[16]</a>.</li> <li><i>The Art of Computer Programming, Volumes 1-3 Boxed Set</i>. Second Edition (Reading, Massachusetts: Addison-Wesley, 1998), pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-201-48541-7, 0-201-48541-9</li> <li><i>The Art of Computer Programming, Volumes 1-4A Boxed Set</i>. Third Edition (Reading, Massachusetts: Addison-Wesley, 2011), 3168pp. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-321-75104-1, 0-321-75104-3</li></ul> <h4>Fascicles</h4> <p>Volume 4, <a href="/facts/Fascicle_(book)/av8UM4vT">Fascicles</a> 0–4 were revised and published as Volume 4A. </p> <ul><li><i>Volume 4, Fascicle 0: Introduction to Combinatorial Algorithms and Boolean Functions</i>. (Addison-Wesley Professional, 2008-04-28) vi+240pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-321-53496-4. Errata: <a href="https://cs.stanford.edu/~knuth/all4f0.ps.gz">[17]</a> (2011-01-01).</li> <li><i>Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams</i>. (Addison-Wesley Professional, 2009-03-27) viii+260pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-321-58050-8. Errata: <a href="https://cs.stanford.edu/~knuth/all4f1.ps.gz">[18]</a> (2011-01-01).</li> <li><i>Volume 4, Fascicle 2: Generating All Tuples and Permutations</i>. (Addison-Wesley, 2005-02-14) v+127pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-85393-0. Errata: <a href="https://cs.stanford.edu/~knuth/all4f2.ps.gz">[19]</a> (2011-01-01).</li> <li><i>Volume 4, Fascicle 3: Generating All Combinations and Partitions</i>. (Addison-Wesley, 2005-07-26) vi+150pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-201-85394-9. Errata: <a href="https://cs.stanford.edu/~knuth/all4f3.ps.gz">[20]</a> (2011-01-01).</li> <li><i>Volume 4, Fascicle 4: Generating All Trees; History of Combinatorial Generation</i>. (Addison-Wesley, 2006-02-06) vi+120pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-321-33570-8. Errata: <a href="https://cs.stanford.edu/~knuth/all4f4.ps.gz">[21]</a> (2011-01-01).</li></ul> <p>Volume 4, Fascicles 5–6 were revised and published as Volume 4B. </p> <ul><li><i>Volume 4, Fascicle 5: Mathematical Preliminaries Redux; Backtracking; Dancing Links</i>. (Addison-Wesley, 2019-11-22) xiii+382pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-13-467179-6. Errata: <a href="https://cs.stanford.edu/~knuth/all4f5.ps.gz">[22]</a> (2020-03-27)</li> <li><i>Volume 4, Fascicle 6: Satisfiability</i>. (Addison-Wesley, 2015-12-08) xiii+310pp, <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-13-439760-3. Errata: <a href="https://cs.stanford.edu/~knuth/all4f6.ps.gz">[23]</a> (2020-03-26)</li></ul> <h4>Pre-fascicles</h4> <p>Volume 1 </p> <ul><li>Pre-fascicle <a href="https://cs.stanford.edu/~knuth/fasc1.ps.gz">1</a> was revised and published as Volume 1, fascicle 1.</li></ul> <p>Volume 4 </p> <ul><li><a href="/facts/Pre-fascicle/uww6A6e2">Pre-fascicles</a> <a href="https://cs.stanford.edu/~knuth/fasc0a.ps.gz">0A</a>, <a href="https://cs.stanford.edu/~knuth/fasc0b.ps.gz">0B</a>, and <a href="https://cs.stanford.edu/~knuth/fasc0c.ps.gz">0C</a> were revised and published as Volume 4, fascicle 0.</li> <li>Pre-fascicles <a href="https://cs.stanford.edu/~knuth/fasc1a.ps.gz">1A</a> and <a href="https://cs.stanford.edu/~knuth/fasc1b.ps.gz">1B</a> were revised and published as Volume 4, fascicle 1.</li> <li>Pre-fascicles <a href="https://cs.stanford.edu/~knuth/fasc2a.ps.gz">2A</a> and <a href="https://cs.stanford.edu/~knuth/fasc2b.ps.gz">2B</a> were revised and published as Volume 4, fascicle 2.</li> <li>Pre-fascicles <a href="https://cs.stanford.edu/~knuth/fasc3a.ps.gz">3A</a> and <a href="https://cs.stanford.edu/~knuth/fasc3b.ps.gz">3B</a> were revised and published as Volume 4, fascicle 3.</li> <li>Pre-fascicles <a href="https://cs.stanford.edu/~knuth/fasc4a.ps.gz">4A</a> and <a href="https://cs.stanford.edu/~knuth/fasc4b.ps.gz">4B</a> were revised and published as Volume 4, fascicle 4.</li> <li>Pre-fascicles <a href="https://cs.stanford.edu/~knuth/fasc5a.ps.gz">5A</a>, <a href="https://cs.stanford.edu/~knuth/fasc5b.ps.gz">5B</a>, and <a href="https://cs.stanford.edu/~knuth/fasc5c.ps.gz">5C</a> were revised and published as Volume 4, fascicle 5.</li> <li>Pre-fascicle <a href="https://cs.stanford.edu/~knuth/fasc6a.ps.gz">6A</a> was revised and published as Volume 4, fascicle 6.</li> <li>Pre-fascicle <a href="https://cs.stanford.edu/~knuth/fasc7a.ps.gz">7A</a> was revised and published as Volume 4, fascicle 7.</li></ul> <p>The remaining pre-fascicles contain draft material that is set to appear in future fascicles and volumes. </p> <ul><li><i><a href="https://cs.stanford.edu/~knuth/fasc8a.ps.gz">Volume 4, Pre-fascicle 8A: Hamiltonian Paths and Cycles</a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc8b.ps.gz">Volume 4, Pre-fascicle 8B: Cliques</a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc9b.ps.gz">Volume 4, Pre-fascicle 9B: A Potpourri of Puzzles</a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc9c.ps.gz">Volume 4, Pre-fascicle 9C: Estimating Backtrack Costs</a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc12a.ps.gz">Volume 4, Pre-fascicle 12A: Components and Traversal</a> <a href="https://cs.stanford.edu/~knuth/fasc12a+.pdf">(PDF Version) </a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc14a.ps.gz">Volume 4, Pre-fascicle 14A: Bipartite Matching</a></i></li> <li><i><a href="https://cs.stanford.edu/~knuth/fasc16a.ps.gz">Volume 4, Pre-fascicle 16A: Introduction to Recursion</a></i></li></ul> <h2 id="see-also">See also</h2> <ul><li><i><a href="/facts/Introduction_to_Algorithms/o9n7KDsg">Introduction to Algorithms</a></i></li></ul> <p>Notes </p> <p>Citations </p> <p>Sources </p> <ul><li>Slater, Robert (1987). <a href="https://books.google.com/books?id=aWTtMyYmKhUC"><i>Portraits in Silicon</i></a>. MIT Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-262-19262-4.</li> <li><a href="/facts/Dennis_Shasha/BAF4VeVs">Shasha, Dennis</a>; Lazere, Cathy (1995). <a href="https://archive.org/details/isbn_9780387979922"><i>Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists</i></a>. Copernicus. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-97992-1.</li></ul> <h2 id="external-links">External links</h2> <ul><li><a href="https://cs.stanford.edu/~knuth/taocp.html">Overview of topics</a> (Knuth's personal homepage)</li> <li><a href="https://cs.stanford.edu/~knuth/brochure.pdf">Announcement of Volume 1 of 'The Art of Computer Programming'</a></li> <li><a href="https://conservancy.umn.edu/items/9cb164e9-c9df-4e5e-9796-42198627fae5">Oral history interview with Donald E. Knuth</a> at <a href="/facts/Charles_Babbage_Institute/7CbplQuX">Charles Babbage Institute</a>, University of Minnesota, Minneapolis, 2001. Knuth discusses software patenting, <a href="/facts/Structured_programming/zA8b8dP1">structured programming</a>, collaboration and his development of <a href="/facts/TeX/8t3cCBqk">TeX</a>. The oral history discusses the writing of <i>The Art of Computer Programming</i>.</li> <li><a href="https://amturing.acm.org/p3-knuth.pdf">"Robert W Floyd, In Memoriam", by Donald E. Knuth</a>, 2003 - (on the influence of <a href="/facts/Robert_W._Floyd/sTFRb3TH">Bob Floyd</a>)</li> <li><a href="https://softpanorama.org/People/Knuth/taocp.shtml"><i>TAoCP</i> and its Influence of Computer Science (Softpanorama)</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"Kuth's note about his books". Archived from the original on 2025-03-01. Retrieved 2025-03-28. <a href="https://www-cs-faculty.stanford.edu/~knuth/taocp.html#future" target="_blank">https://www-cs-faculty.stanford.edu/~knuth/taocp.html#future</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>"note for box 3, folder 1". Archived from the original on 2019-12-03. Retrieved 2019-12-03. <a href="https://oac.cdlib.org/findaid/ark:/13030/kt2k4035s1/entire_text" target="_blank">https://oac.cdlib.org/findaid/ark:/13030/kt2k4035s1/entire_text</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Pearson InformIT webpage book Content tab. Addison-Wesley Professional. 2022-09-28. ISBN 9780201038064. Archived from the original on 2022-07-19. Retrieved 2022-07-19. <a href="9780201038064" target="_blank">9780201038064</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Pearson InformIT webpage. Addison-Wesley Professional. 2022-09-28. ISBN 9780201038064. Archived from the original on 2022-07-19. Retrieved 2022-07-19. <a href="9780201038064" target="_blank">9780201038064</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"CP 2022 All Questions Answered, July 31–August 5, 2022, Haifa, Israel". Archived from the original on 2022-07-22. Retrieved 2022-07-22. <a href="https://cp2022.a4cp.org/invited.html" target="_blank">https://cp2022.a4cp.org/invited.html</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>Pearson InformIT webpage. Addison-Wesley Professional. 2025-02-05. ISBN 9780135328248. Archived from the original on 2025-02-18. Retrieved 2025-02-18. <a href="9780135328248" target="_blank">9780135328248</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>Frana, Philip L. (2001-11-08). "An Interview with Donald E. Knuth". hdl:11299/107413. Archived from the original on 2018-06-20. Retrieved 2018-06-20. <a href="https://conservancy.umn.edu/handle/11299/107413" target="_blank">https://conservancy.umn.edu/handle/11299/107413</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>Feigenbaum, Edward (2007). "Oral History of Donald Knuth" (PDF). Computer History Museum. Archived (PDF) from the original on 2008-12-09. Retrieved 2024-11-26. <a href="/wiki/Edward_Feigenbaum" target="_blank">/wiki/Edward_Feigenbaum</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>Knuth, Donald E. (1993-08-23). "This Week's Citation Classic" (PDF). Current Contents. p. 8. Archived (PDF) from the original on 2024-01-05. 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