Best, worst and average case

In computer science, best, worst, and average cases of a given algorithm express what the resource usage is at least, at most and on average, respectively. Usually the resource being considered is running time, i.e. time complexity, but it could also be memory or other resource.

In real-time computing, the worst-case execution time is often of particular concern since it is important to know how much time might be needed in the worst case to guarantee that the algorithm will always finish on time.

Average performance and worst-case performance are the most used in algorithm analysis. Less widely found is best-case performance, but it does have uses: for example, where the best cases of individual tasks are known, they can be used to improve the accuracy of an overall worst-case analysis. Computer scientists use probabilistic analysis techniques, especially expected value, to determine expected running times.

The terms are used in other contexts; for example the worst- and best-case outcome of a planned-for epidemic, worst-case temperature to which an electronic circuit element is exposed, etc. Where components of specified tolerance are used, devices must be designed to work properly with the worst-case combination of tolerances and external conditions.

The term best-case performance is used in computer science to describe an algorithm's behavior under optimal conditions. For example, the best case for a simple linear search on a list occurs when the desired element is the first element of the list.

Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving Average-case complexity and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the measure almost meaningless.

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