Editing Algorithm (section)

== Design ==
{{See also|Algorithm#By design paradigm}}

Algorithm design is a method or mathematical process for problem-solving and engineering algorithms. The design of algorithms is part of many solution theories, such as [[divide-and-conquer algorithm|divide-and-conquer]] or [[dynamic programming]] within [[operation research]]. Techniques for designing and implementing algorithm designs are also called algorithm design patterns,<ref>{{cite book |last1=Goodrich |first1=Michael T. |author1-link=Michael T. Goodrich |url=http://ww3.algorithmdesign.net/ch00-front.html |title=Algorithm Design: Foundations, Analysis, and Internet Examples |last2=Tamassia |first2=Roberto |author2-link=Roberto Tamassia |publisher=John Wiley & Sons, Inc. |year=2002 |isbn=978-0-471-38365-9 |access-date=June 14, 2018 |archive-url=https://web.archive.org/web/20150428201622/http://ww3.algorithmdesign.net/ch00-front.html |archive-date=April 28, 2015 |url-status=live}}</ref> with examples including the template method pattern and the decorator pattern. One of the most important aspects of algorithm design is resource (run-time, memory usage) efficiency; the [[big O notation]] is used to describe e.g., an algorithm's run-time growth as the size of its input increases.<ref>{{Cite web |title=Big-O notation (article) {{!}} Algorithms |url=https://www.khanacademy.org/computing/computer-science/algorithms/asymptotic-notation/a/big-o-notation |access-date=2024-06-03 |website=Khan Academy |language=en}}</ref>

=== Structured programming ===
Per the [[Church–Turing thesis]], any algorithm can be computed by any [[Turing complete]] model. Turing completeness only requires four instruction types—conditional GOTO, unconditional GOTO, assignment, HALT. However, Kemeny and Kurtz observe that, while "undisciplined" use of unconditional GOTOs and conditional IF-THEN GOTOs can result in "[[spaghetti code]]", a programmer can write structured programs using only these instructions; on the other hand "it is also possible, and not too hard, to write badly structured programs in a structured language".<ref>[[John G. Kemeny]] and [[Thomas E. Kurtz]] 1985 ''Back to Basic: The History, Corruption, and Future of the Language'', Addison-Wesley Publishing Company, Inc. Reading, MA, {{ISBN|0-201-13433-0}}.</ref> Tausworthe augments the three [[Structured program theorem|Böhm-Jacopini canonical structures]]:<ref>Tausworthe 1977:101</ref> SEQUENCE, IF-THEN-ELSE, and WHILE-DO, with two more: DO-WHILE and CASE.<ref>Tausworthe 1977:142</ref> An additional benefit of a structured program is that it lends itself to [[proof of correctness|proofs of correctnes]]s using [[mathematical induction]].<ref>Knuth 1973 section 1.2.1, expanded by Tausworthe 1977 at pages 100ff and Chapter 9.1</ref>