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The Art of Computer Programming
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====Volume 1 β Fundamental algorithms==== * Chapter 1 β Basic concepts ** 1.1. [[Algorithm]]s ** 1.2. Mathematical preliminaries *** 1.2.1. [[Mathematical induction]] *** 1.2.2. Numbers, powers, and [[logarithm]]s *** 1.2.3. Sums and products *** 1.2.4. Integer functions and elementary [[number theory]] *** 1.2.5. [[Permutation]]s and [[factorial]]s *** 1.2.6. [[Binomial coefficient]]s *** 1.2.7. [[Harmonic number]]s *** 1.2.8. [[Fibonacci number]]s *** 1.2.9. [[Generating function]]s *** 1.2.10. Analysis of an algorithm *** 1.2.11. [[Asymptotic analysis|Asymptotic representations]] **** 1.2.11.1. The [[Big O notation|O-notation]] **** 1.2.11.2. [[Euler's summation formula]] **** 1.2.11.3. Some asymptotic calculations ** 1.3 [[MIX (abstract machine)|MIX]] (Updated with [[MMIX]]<ref>{{cite web |url=https://www-cs-faculty.stanford.edu/~knuth/taocp.html#future |title=Kuth's future editions Volumes 1-3 |access-date=2025-04-25 |archive-date=2025-04-23 |archive-url=https://web.archive.org/web/20250423130634/https://www-cs-faculty.stanford.edu/~knuth/taocp.html#future |url-status=live }}</ref> in Volume 1 fascicle 1) *** 1.3.1. Description of MIX *** 1.3.2. The MIX assembly language *** 1.3.3. Applications to [[permutation]]s ** 1.4. Some fundamental programming techniques *** 1.4.1. [[Function (computer programming)|Subroutines]] *** 1.4.2. [[Coroutine]]s *** 1.4.3. Interpretive routines **** 1.4.3.1. A MIX simulator **** 1.4.3.2. Trace routines *** 1.4.4. [[Input/output|Input and output]] *** 1.4.5. History and bibliography * Chapter 2 β Information structures ** 2.1. Introduction ** 2.2. [[List (abstract data type)|Linear lists]] *** 2.2.1. [[Stack (abstract data type)|Stacks]], [[Queue (abstract data type)|queues]], and [[Double-ended queue|deques]] *** 2.2.2. Sequential allocation *** 2.2.3. Linked allocation ([[topological sorting]]) *** 2.2.4. Circular lists *** 2.2.5. Doubly linked lists *** 2.2.6. [[Array (data structure)|Arrays]] and orthogonal lists ** 2.3. [[Tree (data structure)|Trees]] *** 2.3.1. Traversing [[binary tree]]s *** 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. [[Polytree|Oriented trees]] **** 2.3.4.3. [[KΕnig's lemma|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 (computer science)|garbage collection]] ** 2.4. Multilinked structures ** 2.5. [[Dynamic memory allocation|Dynamic storage allocation]] ** 2.6. History and bibliography
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