The number of symbol comparisons in quicksort and quickselect

Abstract

We revisit the classical QuickSort and QuickSelect algorithms, under a complexity model that fully takes into account the elementary comparisons between symbols composing the records to be processed. Our probabilistic models belong to a broad category of information sources that encompasses memoryless (i.e., independent-symbols) and Markov sources, as well as many unbounded-correlation sources. We establish that, under our conditions, the average-case complexity of QuickSort is O(nlog2 n) [rather than O(nlogn), classically], whereas that of QuickSelect remains O(n). Explicit expressions for the implied constants are provided by our combinatorial-analytic methods. © 2009 Springer Berlin Heidelberg.