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.\"	$OpenBSD: qsort.3,v 1.20 2017/05/20 13:09:01 millert Exp $
.\"
.Dd $Mdocdate: May 20 2017 $
.Dt QSORT 3
.Os
.Sh NAME
.Nm qsort ,
.Nm heapsort ,
.Nm mergesort
.Nd sort functions
.Sh SYNOPSIS
.In stdlib.h
.Ft void
.Fn qsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
.Ft int
.Fn heapsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
.Ft int
.Fn mergesort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)"
.Sh DESCRIPTION
The
.Fn qsort
function is a modified partition-exchange sort, or quicksort.
The
.Fn heapsort
function is a modified selection sort.
The
.Fn mergesort
function is a modified merge sort with exponential search
intended for sorting data with pre-existing order.
.Pp
The
.Fn qsort
and
.Fn heapsort
functions sort an array of
.Fa nmemb
objects, the initial member of which is pointed to by
.Fa base .
The size of each object is specified by
.Fa size .
.Fn mergesort
behaves similarly, but
.Em requires
that
.Fa size
be greater than
.Dq "sizeof(void *) / 2" .
.Pp
The contents of the array
.Fa base
are sorted in ascending order according to
a comparison function pointed to by
.Fa compar ,
which requires two arguments pointing to the objects being
compared.
.Pp
The comparison function must return an integer less than, equal to, or
greater than zero if the first argument is considered to be respectively
less than, equal to, or greater than the second.
.Pp
The functions
.Fn qsort
and
.Fn heapsort
are
.Em not
stable, that is, if two members compare as equal, their order in
the sorted array is undefined.
The function
.Fn mergesort
is stable.
.Pp
The
.Fn qsort
function is an implementation of C.A.R. Hoare's
.Dq quicksort
algorithm,
a variant of partition-exchange sorting; in particular, see D.E. Knuth's
Algorithm Q.
.Fn qsort
takes O N lg N average time.
This implementation uses median selection to avoid its
O N**2 worst-case behavior and will fall back to
.Fn heapsort
if the recursion depth exceeds 2 lg N.
.Pp
The
.Fn heapsort
function is an implementation of J.W.J. William's
.Dq heapsort
algorithm,
a variant of selection sorting; in particular, see D.E. Knuth's Algorithm H.
.Fn heapsort
takes O N lg N worst-case time.
This implementation of
.Fn heapsort
is implemented without recursive function calls.
.Pp
The function
.Fn mergesort
requires additional memory of size
.Fa nmemb *
.Fa size
bytes; it should be used only when space is not at a premium.
.Fn mergesort
is optimized for data with pre-existing order; its worst case
time is O N lg N; its best case is O N.
.Pp
Normally,
.Fn qsort
is faster than
.Fn mergesort ,
which is faster than
.Fn heapsort .
Memory availability and pre-existing order in the data can make this untrue.
.Sh RETURN VALUES
.Rv -std heapsort mergesort
.Sh ERRORS
The
.Fn heapsort
and
.Fn mergesort
functions succeed unless:
.Bl -tag -width Er
.It Bq Er EINVAL
The
.Fa size
argument is zero, or the
.Fa size
argument to
.Fn mergesort
is less than
.Dq "sizeof(void *) / 2" .
.It Bq Er ENOMEM
.Fn heapsort
or
.Fn mergesort
were unable to allocate memory.
.El
.Sh SEE ALSO
.Xr sort 1 ,
.Xr radixsort 3
.Rs
.%A Hoare, C.A.R.
.%D 1962
.%T "Quicksort"
.%J "The Computer Journal"
.%V 5:1
.%P pp. 10-15
.Re
.Rs
.%A Williams, J.W.J
.%D 1964
.%T "Heapsort"
.%J "Communications of the ACM"
.%V 7:1
.%P pp. 347\-348
.Re
.Rs
.%A Knuth, D.E.
.%D 1968
.%B "The Art of Computer Programming"
.%V Vol. 3
.%T "Sorting and Searching"
.%P pp. 114\-123, 145\-149
.Re
.Rs
.%A McIlroy, P.M.
.%T "Optimistic Sorting and Information Theoretic Complexity"
.%J "Fourth Annual ACM-SIAM Symposium on Discrete Algorithms"
.%P pp. 467\-464
.%D January 1993
.Re
.Rs
.%A Bentley, J.L.
.%A McIlroy, M.D.
.%T "Engineering a Sort Function"
.%J "Software \- Practice and Experience"
.%V Vol. 23(11)
.%P pp. 1249\-1265
.%D November 1993
.Re
.Rs
.%A Musser, D.
.%T "Introspective Sorting and Selection Algorithms"
.%J "Software \- Practice and Experience"
.%V Vol. 27(8)
.%P pp. 983\-993
.%D August 1997
.Re
.Sh STANDARDS
Previous versions of
.Fn qsort
did not permit the comparison routine itself to call
.Fn qsort .
This is no longer true.
.Pp
The
.Fn qsort
function conforms to
.St -ansiC .
.Sh HISTORY
A
.Fn qsort
function first appeared in
.At v3 .