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25.1 What is efficiency?

The standard algorithm analyses in computer science measure efficiency asymptotically as a function of problem size (such as data, number of parameters, etc.) and typically do not consider constant additive factors like startup times or multiplicative factors like speed of operations. In practice, the constant factors are important; if run time can be cut in half or more, that’s a huge gain. This chapter focuses on both the constant factors involved in efficiency (such as using built-in matrix operations as opposed to naive loops) and on asymptotic efficiency factors (such as using linear algorithms instead of quadratic algorithms in loops).