Abstract
Mellin transforms and Dirichlet series are useful in quantifying periodicity phenomena present in recursive divide-and-conquer algorithms. This note illustrates the techniques by providing a precise analysis of the standard topdown recursive mergesort algorithm, in the average case, as well as in the worst and best cases. It also derives the variance and shows that the cost of mergesort has a Gaussian limiting distribution. The approach is applicable to a number of divide-and-conquer recurrences.
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Flajolet, P., Golin, M. Mellin transforms and asymptotics. Acta Informatica 31, 673–696 (1994). https://doi.org/10.1007/BF01177551
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DOI: https://doi.org/10.1007/BF01177551