Abstract
Using Fourier analysis, we prove that the limiting distribution of the standardized random number of comparisons used by Quicksort to sort an array of n numbers has an everywhere positive and infinitely differentiable density f, and that each derivative f (k) enjoys superpolynomial decay at ±∞. In particular, each f (k) is bounded. Our method is sufficiently computational to prove, for example, that f is bounded by 16.
1Research supported by NSF grant DMS-9803780, and by the Acheson J. Duncan Fund for the Advancement of Research in Statistics.
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Fill, J.A., Janson, S. (2000). Smoothness and Decay Properties of the Limiting Quicksort Density Function. In: Gardy, D., Mokkadem, A. (eds) Mathematics and Computer Science. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8405-1_5
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DOI: https://doi.org/10.1007/978-3-0348-8405-1_5
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