# The number of comparisons in QuickSort

 Title: The number of comparisons in QuickSort Author: Manuel Eberl Submission date: 2017-03-15 Abstract: We give a formal proof of the well-known results about the number of comparisons performed by two variants of QuickSort: first, the expected number of comparisons of randomised QuickSort (i. e. QuickSort with random pivot choice) is 2 (n+1) Hn - 4 n, which is asymptotically equivalent to 2 n ln n; second, the number of comparisons performed by the classic non-randomised QuickSort has the same distribution in the average case as the randomised one. BibTeX: @article{Quick_Sort_Cost-AFP, author = {Manuel Eberl}, title = {The number of comparisons in QuickSort}, journal = {Archive of Formal Proofs}, month = mar, year = 2017, note = {\url{https://isa-afp.org/entries/Quick_Sort_Cost.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Comparison_Sort_Lower_Bound, Landau_Symbols, List-Index, Regular-Sets Used by: Random_BSTs Status: [ok] This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.