Dual pivot Quicksort

TL;DR

This paper provides a detailed analysis of dual pivot Quicksort, calculating its expected comparisons, exchanges, and variance, revealing that it does not outperform standard Quicksort in average case speed.

Contribution

The paper offers the first exact and asymptotic analysis of dual pivot Quicksort's key comparisons and exchanges, including variance and partitioning stages.

Findings

Dual pivot Quicksort has similar average comparison counts as standard Quicksort.

The variance of key comparisons in dual pivot Quicksort is quantified.

Average number of partitioning stages is computed for the dual pivot variant.

Abstract

In this paper, we analyse the dual pivot Quicksort, a variant of the standard Quicksort algorithm, in which two pivots are used for the partitioning of the array. We are solving recurrences of the expected number of key comparisons and exchanges performed by the algorithm, obtaining the exact and asymptotic total average values contributing to its time complexity. Further, we compute the average number of partitioning stages and the variance of the number of key comparisons. In terms of mean values, dual pivot Quicksort does not appear to be faster than ordinary algorithm.