Increasing the Efficiency of Quicksort
A method is presented for the analysis of various generalizations of
quicksort.  The average asymptotic number of comparisons needed is shown
 to be an log^2(n).  A formula is derived expressing a in terms of
the probability distribution of the "bound" of a partition.  This
 formula assumes a particularly simple form for a generalization already
considered by Hoare, namely, choice of the bound as median
of a random sample. The main contribution of this paper is another
generalization of quicksort, which uses a bounding interval instead
of a single element as bound.  This generalization turns out to
be easy to implement in a computer program.  A numerical approximation
shows that a = 1.140 for this version of quicksort compared with
1.386 for the original.  This implies a decrease in number of comparisons of 
18 percent; actual tests showed about 15 percent saving in computing time.
CACM September, 1970
van Emden, M. H.
