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A note on the Quicksort asymptotics. (English) Zbl 1332.68039
Summary: In a recent paper, P. Bindjeme and J. A. Fill [in: Proceeding of the 23rd international meeting on probabilistic, combinatorial, and asymptotic methods in the analysis of algorithms, AofA’12. Nancy: The Association. Discrete Mathematics & Theoretical Computer Science (DMTCS). 339–348 (2012; Zbl 1296.68039)] obtained a surprisingly easy exact formula for the \(L_{2}\)-distance of the (normalized) number of comparisons of Quicksort under the uniform model to its limit. Shortly afterwards, R. Neininger proved [Random Struct. Algorithms 46, No. 2, 346–361 (2015; Zbl 1327.68086)] a central limit theorem for the error. As a consequence, he obtained the asymptotics of the \(L_{3}\)-distance. In this short note, we use the moment transfer approach to re-prove Neininger’s result. As a consequence, we obtain the asymptotics of the \(L_{p}\)-distance for all \(1\leq p<\infty\).

MSC:
68P10 Searching and sorting
60G42 Martingales with discrete parameter
Software:
Quicksort
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References:
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