Abstract
A fine analysis is given of the transitional behavior of the average cost of quicksort with median-of-three. Asymptotic formulae are derived for the stepwise improvement of the average cost of quicksort when iterating median-of-threek rounds for all possible values ofk. The methods used are general enough to apply to quicksort with median-of-(2t + 1) and to explain in a precise manner the transitional behaviors of the average cost from insertion sort to quicksort proper. Our results also imply nontrivial bounds on the expected height, “saturation level,” and width in a random locally balanced binary search tree.
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Communicated by H. Prodinger and W. Szpankowski.
This work was done while the first author was at the Institute of Mathematics, Academia Sinica, Taipei, Taiwan.
Online publication September 22, 2000.
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Chern, H.H., Hwang, H.K. Transitional behaviors of the average cost of quicksort with median-of-(2t + 1). Algorithmica 29, 44–69 (2001). https://doi.org/10.1007/BF02679613
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DOI: https://doi.org/10.1007/BF02679613