Quicksort with Equal Keys

Abstract

This paper considers the problem of implementing and analyzing a Quicksort program when equal keys are likely to be present in the file to be sorted. Upper and lower bounds are derived on the average number of comparisons needed by any Quicksort program when equal keys are present. It is shown that, of the three strategies which have been suggested for dealing with equal keys, the method of always stopping the scanning pointers on keys equal to the partitioning element performs best.