Algorithm: Difference between revisions

Revision as of 22:42, 26 January 2025

Revision as of 21:02, 31 January 2025

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==Representations==

Algorithms can be expressed in many kinds of notation, including [[natural languages]], [[pseudocode]], [[flowchart]]s, [[DRAKON|drakon-chart]]s, [[programming languages]] or [[control table]]s (processed by [[Interpreter (computing)|interpreter]]s). Natural language expressions of algorithms tend to be verbose and ambiguous and are rarely used for complex or technical algorithms. Pseudocode, flowcharts, drakon-charts, and control tables are structured expressions of algorithms that avoid common ambiguities of natural language. Programming languages are primarily for expressing algorithms in a computer-executable form, but are also used to define or document algorithms.

=== Turing machines ===

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{{Main|Empirical algorithmics|Profiling (computer programming)|Program optimization}}

The [[analysis of algorithms|analysis, and study of algorithm]]s is a discipline of [[computer science]]. Algorithms are often studied abstractly, without referencing any specific [[programming language]] or implementation. Algorithm analysis resembles other mathematical disciplines as it focuses on the algorithm's properties, not implementation. [[Pseudocode]] is typical for analysis as it is a simple and general representation. Most algorithms are implemented on particular hardware/software platforms and their [[algorithmic efficiency]] is tested using real code. The efficiency of a particular algorithm may be insignificant for many "one-off" problems but it may be critical for algorithms designed for fast interactive, commercial, or long -life scientific usage. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign.

Empirical testing is useful for uncovering unexpected interactions that affect performance. [[Benchmark (computing)|Benchmark]]s may be used to compare before/after potential improvements to an algorithm after program optimization.

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: While many algorithms reach an exact solution, [[approximation algorithm]]s seek an approximation that is close to the true solution. Such algorithms have practical value for many hard problems. For example, the [[Knapsack problem]], where there is a set of items and the goal is to pack the knapsack to get the maximum total value. Each item has some weight and some value. The total weight that can be carried is no more than some fixed number X. So, the solution must consider weights of items as well as their value.<ref>{{Cite book|url=https://www.springer.com/us/book/9783540402862|title=Knapsack Problems {{!}} Hans Kellerer {{!}} Springer|language=en|isbn=978-3-540-40286-2|publisher=Springer|year=2004|doi=10.1007/978-3-540-24777-7|access-date=September 19, 2017|archive-url=https://web.archive.org/web/20171018181055/https://www.springer.com/us/book/9783540402862|archive-date=October 18, 2017|url-status=live|last1=Kellerer|first1=Hans|last2=Pferschy|first2=Ulrich|last3=Pisinger|first3=David|s2cid=28836720 }}</ref>

; Quantum algorithm

: [[Quantum algorithm]]s run on a realistic model of [[quantum computation]]. The term is usually used for those algorithms whichthat seem inherently quantum or use some essential feature of [[Quantum computing]] such as [[quantum superposition]] or [[quantum entanglement]].

=== By design paradigm ===