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.\"     @(#)qsort.3	8.1 (Berkeley) 6/4/93
.\" $FreeBSD: head/lib/libc/stdlib/qsort.3 298201 2016-04-18 09:56:41Z pluknet $
.\"
.Dd February 20, 2013
.Dt QSORT 3
.Os
.Sh NAME
.Nm qsort , qsort_b , qsort_r , heapsort , heapsort_b , mergesort, mergesort_b
.Nd sort functions
.Sh LIBRARY
.Lb libc
.Sh SYNOPSIS
.In stdlib.h
.Ft void
.Fo qsort
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]*compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft void
.Fo qsort_b
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]^compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft void
.Fo qsort_r
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "void *thunk"
.Fa "int \*[lp]*compar\*[rp]\*[lp]void *, const void *, const void *\*[rp]"
.Fc
.Ft int
.Fo heapsort
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]*compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft int
.Fo heapsort_b
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]^compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft int
.Fo mergesort
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]*compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.Ft int
.Fo mergesort_b
.Fa "void *base"
.Fa "size_t nmemb"
.Fa "size_t size"
.Fa "int \*[lp]^compar\*[rp]\*[lp]const void *, const void *\*[rp]"
.Fc
.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 .
The
.Fn mergesort
function
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
.Fn qsort_r
function behaves identically to
.Fn qsort ,
except that it takes an additional argument,
.Fa thunk ,
which is passed unchanged as the first argument to function pointed to
.Fa compar .
This allows the comparison function to access additional
data without using global variables, and thus
.Fn qsort_r
is suitable for use in functions which must be reentrant.
The
.Fn qsort_b
function behaves identically to
.Fn qsort ,
except that it takes a block, rather than a function pointer.
.Pp
The algorithms implemented by
.Fn qsort ,
.Fn qsort_r ,
and
.Fn heapsort
are
.Em not
stable, that is, if two members compare as equal, their order in
the sorted array is undefined.
The
.Fn heapsort_b
function behaves identically to
.Fn heapsort ,
except that it takes a block, rather than a function pointer.
The
.Fn mergesort
algorithm is stable.
The
.Fn mergesort_b
function behaves identically to
.Fn mergesort ,
except that it takes a block, rather than a function pointer.
.Pp
The
.Fn qsort
and
.Fn qsort_r
functions are an implementation of C.A.R.
Hoare's
.Dq quicksort
algorithm,
a variant of partition-exchange sorting; in particular, see
.An D.E. Knuth Ns 's
.%T "Algorithm Q" .
.Sy Quicksort
takes O N lg N average time.
This implementation uses median selection to avoid its
O N**2 worst-case behavior.
.Pp
The
.Fn heapsort
function is an implementation of
.An "J.W.J. William" Ns 's
.Dq heapsort
algorithm,
a variant of selection sorting; in particular, see
.An "D.E. Knuth" Ns 's
.%T "Algorithm H" .
.Sy Heapsort
takes O N lg N worst-case time.
Its
.Em only
advantage over
.Fn qsort
is that it uses almost no additional memory; while
.Fn qsort
does not allocate memory, it is implemented using recursion.
.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.
The
.Fn mergesort
function
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
is faster than
.Fn heapsort .
Memory availability and pre-existing order in the data can make this
untrue.
.Sh RETURN VALUES
The
.Fn qsort
and
.Fn qsort_r
functions
return no value.
.Pp
.Rv -std heapsort mergesort
.Sh EXAMPLES
A sample program that sorts an array of
.Vt int
values in place using
.Fn qsort ,
and then prints the sorted array to standard output is:
.Bd -literal
#include <stdio.h>
#include <stdlib.h>

/*
 * Custom comparison function that compares 'int' values through pointers
 * passed by qsort(3).
 */
static int
int_compare(const void *p1, const void *p2)
{
	int left = *(const int *)p1;
	int right = *(const int *)p2;

	return ((left > right) - (left < right));
}

/*
 * Sort an array of 'int' values and print it to standard output.
 */
int
main(void)
{
	int int_array[] = { 4, 5, 9, 3, 0, 1, 7, 2, 8, 6 };
	size_t array_size = sizeof(int_array) / sizeof(int_array[0]);
	size_t k;

	qsort(&int_array, array_size, sizeof(int_array[0]), int_compare);
	for (k = 0; k < array_size; k++)
		printf(" %d", int_array[k]);
	puts("");
	return (EXIT_SUCCESS);
}
.Ed
.Sh COMPATIBILITY
Previous versions of
.Fn qsort
did not permit the comparison routine itself to call
.Fn qsort 3 .
This is no longer true.
.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
The
.Fn heapsort
or
.Fn mergesort
functions
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"
.%V January 1992
.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
.Sh STANDARDS
The
.Fn qsort
function
conforms to
.St -isoC .
.Sh HISTORY
The variants of these functions that take blocks as arguments first appeared in
Mac OS X.
This implementation was created by David Chisnall.