Heapsort man page on 4.4BSD

```QSORT(3)		    BSD Programmer's Manual		      QSORT(3)

NAME
qsort, heapsort, mergesort - sort functions

SYNOPSIS
#include <stdlib.h>

void
qsort(void *base, size_t nmemb, size_t size,
int (*compar)(const void *, const void *));

int
heapsort(void *base, size_t nmemb, size_t size,
int (*compar)(const void *, const void *));

int
mergesort(void *base, size_t nmemb, size_t size,
int (*compar)(const void *, const void *));

DESCRIPTION
The qsort() function is a modified partition-exchange sort, or quicksort.
The heapsort() function is a modified selection sort.  The mergesort()
function is a modified merge sort with exponential search intended for
sorting data with pre-existing order.

The qsort() and heapsort() functions sort an array of nmemb objects, the
initial member of which is pointed to by base. The size of each object is
specified by size. Mergesort() behaves similarly, but requires that size
be greater than ``sizeof(void *) / 2''.

The contents of the array base are sorted in ascending order according to
a comparison function pointed to by compar, which requires two arguments
pointing to the objects being compared.

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.

The functions qsort() and heapsort() are not stable, that is, if two mem-
bers compare as equal, their order in the sorted array is undefined.  The
function mergesort() is stable.

The qsort() function is an implementation of C.A.R. Hoare's ``quicksort''
algorithm, a variant of partition-exchange sorting; in particular, see
D.E. Knuth's Algorithm Q.	Qsort() takes O N lg N average time.  This im-
plementation uses median selection to avoid its O N**2 worst-case behav-
ior.

The heapsort() function is an implementation of J.W.J. William's ``heap-
sort'' algorithm, a variant of selection sorting; in particular, see D.E.
Knuth's Algorithm H.  Heapsort() takes O N lg N worst-case time.  Its
only advantage over qsort() is that it uses almost no additional memory;
while qsort() does not allocate memory, it is implemented using recur-
sion.

The function mergesort() requires additional memory of size nmemb * size
bytes; it should be used only when space is not at a premium.
Mergesort() is optimized for data with pre-existing order; its worst case
time is O N lg N; its best case is O N.

Normally, qsort() is faster than mergesort() is faster than heapsort().
Memory availability and pre-existing order in the data can make this un-
true.

RETURN VALUES
The qsort() function returns no value.

Upon successful completion, heapsort() and mergesort() return 0.  Other-
wise, they return -1 and the global variable errno is set to indicate the
error.

ERRORS
The heapsort() function succeeds unless:

[EINVAL]	   The size argument is zero, or, the size argument to
mergesort() is less than ``sizeof(void *) / 2''.

[ENOMEM]	   Heapsort() or mergesort() were unable to allocate memory.

COMPATIBILITY
Previous versions of qsort() did not permit the comparison routine itself
to call qsort(3).	This is no longer true.

Hoare, C.A.R., "Quicksort", The Computer Journal, 5:1, pp. 10-15, 1962.

Williams, J.W.J, "Heapsort", Communications of the ACM, 7:1, pp. 347-348,
1964.

Knuth, D.E., "Sorting and Searching", The Art of Computer Programming,
Vol. 3, pp. 114-123, 145-149, 1968.

Mcilroy, P.M., "Optimistic Sorting and Information Theoretic Complexity",
Fourth Annual ACM-SIAM Symposium on Discrete Algorithms, January 1992.

Bentley, J.L., "Engineering a Sort Function", bentley@research.att.com,
January 1992.

STANDARDS
The qsort() function conforms to ANSI C X3.159-1989 (``ANSI C '').

4.4BSD				 June 4, 1993				     2
```
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