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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 could also be memory or some other resource. Best case is the function which performs the minimum number of ...
Linear time is the best possible time complexity in situations where the algorithm has to sequentially read its entire input. Therefore, much research has been invested into discovering algorithms exhibiting linear time or, at least, nearly linear time.
The order of growth (e.g. linear, logarithmic) of the worst-case complexity is commonly used to compare the efficiency of two algorithms. The worst-case complexity of an algorithm should be contrasted with its average-case complexity, which is an average measure of the amount of resources the algorithm uses on a random input.
The best, worst and average case complexity refer to three different ways of measuring the time complexity (or any other complexity measure) of different inputs of the same size. Since some inputs of size n {\displaystyle n} may be faster to solve than others, we define the following complexities:
Comparison column has the following ranking classifications: "Best", "Average" and "Worst" if the time complexity is given for each case. "Memory" denotes the amount of additional storage required by the algorithm. The run times and the memory requirements listed are inside big O notation, hence the base of the logarithms does not matter.
The worst-case complexity is the maximum of the complexity over all inputs of size n, and the average-case complexity is the average of the complexity over all inputs of size n (this makes sense, as the number of possible inputs of a given size is finite). Generally, when "complexity" is used without being further specified, this is the worst ...
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In such cases, the worst-case running time can be much worse than the observed running time in practice. For example, the worst-case complexity of solving a linear program using the simplex algorithm is exponential, [2] although the observed number of steps in practice is roughly linear. [3] [4] The simplex algorithm is in fact much faster than ...