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Efficiency looks at how much time it takes to run a particular algorithm and how much space is needed. By using both measurements, an algorithm that looks much more complex can actually be more efficient. ... Efficiency looks at how much time it takes to run a particular algorithm and how much space is needed.
The importance of efficiency with respect to time was emphasised by Ada Lovelace in 1843 as applying to Charles Babbage's mechanical analytical engine:
"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"
Early electronic computers were severely limited both by the speed of operations and the amount of memory available. In some cases it was realized that there was a space–time trade-off, whereby a task could be handled either by using a fast algorithm which used quite a lot of working memory, or by using a slower algorithm which used very little working memory. The engineering trade-off was then to use the fastest algorithm which would fit in the available memory.