Editing Algorithmic efficiency (section)

==Background==
The importance of efficiency with respect to time was emphasized by [[Ada Lovelace]] in 1843 as applied to [[Charles Babbage]]'s mechanical analytical engine:
<blockquote>"In almost every computation a great variety of arrangements for the succession of the processes is possible, and various considerations must influence the selections amongst them for the purposes of a calculating engine. One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation"<ref>{{
Citation
 | last1 = Green | first1 = Christopher
 | title = Classics in the History of Psychology
 | url  = http://psychclassics.yorku.ca/Lovelace/lovelace.htm
 | access-date = 19 May 2013
}}</ref></blockquote>

Early [[electronic computer]]s had both limited [[clock cycle|speed]] and limited [[random access memory]]. Therefore, a [[space–time trade-off]] occurred. A [[Task (computing)|task]] could use a fast algorithm using a lot of memory, or it could use a slow algorithm using little memory. The engineering trade-off was therefore to use the fastest algorithm that could fit in the available memory.

Modern computers are significantly faster than early computers and have a much larger amount of memory available ([[Orders of magnitude (computing)|gigabytes instead of kilobytes]]). Nevertheless, [[Donald Knuth]] emphasized that efficiency is still an important consideration:

 <blockquote> "In established engineering disciplines a 12% improvement, easily obtained, is never considered marginal and I believe the same viewpoint should prevail in software engineering"<ref name="Knuth1974">{{
Citation
 |last1=Knuth 
 |first1=Donald 
 |title=Structured Programming with go-to Statements 
 |journal=Computing Surveys 
 |volume=6 
 |issue=4 
 |pages=261–301 
 |year=1974 
 |url=http://pplab.snu.ac.kr/courses/adv_pl05/papers/p261-knuth.pdf 
 |access-date=19 May 2013 
 |url-status=dead 
 |archive-url=https://web.archive.org/web/20090824073244/http://pplab.snu.ac.kr/courses/adv_pl05/papers/p261-knuth.pdf 
 |archive-date=24 August 2009 
|doi=10.1145/356635.356640 
 |citeseerx=10.1.1.103.6084 
 |s2cid=207630080 
 }}</ref></blockquote>