1.\" Copyright (c) 1990, 1991, 1993 2.\" The Regents of the University of California. All rights reserved. 3.\" 4.\" This code is derived from software contributed to Berkeley by 5.\" the American National Standards Committee X3, on Information 6.\" Processing Systems. 7.\" 8.\" Redistribution and use in source and binary forms, with or without 9.\" modification, are permitted provided that the following conditions 10.\" are met: 11.\" 1. Redistributions of source code must retain the above copyright 12.\" notice, this list of conditions and the following disclaimer. 13.\" 2. Redistributions in binary form must reproduce the above copyright 14.\" notice, this list of conditions and the following disclaimer in the 15.\" documentation and/or other materials provided with the distribution. 16.\" 3. All advertising materials mentioning features or use of this software 17.\" must display the following acknowledgement: 18.\" This product includes software developed by the University of 19.\" California, Berkeley and its contributors. 20.\" 4. Neither the name of the University nor the names of its contributors 21.\" may be used to endorse or promote products derived from this software 22.\" without specific prior written permission. 23.\" 24.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 25.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 26.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 27.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 28.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 29.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 30.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 31.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 32.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 33.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 34.\" SUCH DAMAGE. 35.\" 36.\" $OpenBSD: qsort.3,v 1.6 2000/08/09 15:51:21 aaron Exp $ 37.\" 38.Dd June 4, 1993 39.Dt QSORT 3 40.Os 41.Sh NAME 42.Nm qsort , 43.Nm heapsort , 44.Nm mergesort 45.Nd sort functions 46.Sh SYNOPSIS 47.Fd #include <stdlib.h> 48.Ft void 49.Fn qsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)" 50.Ft int 51.Fn heapsort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)" 52.Ft int 53.Fn mergesort "void *base" "size_t nmemb" "size_t size" "int (*compar)(const void *, const void *)" 54.Sh DESCRIPTION 55The 56.Fn qsort 57function is a modified partition-exchange sort, or quicksort. 58The 59.Fn heapsort 60function is a modified selection sort. 61The 62.Fn mergesort 63function is a modified merge sort with exponential search 64intended for sorting data with pre-existing order. 65.Pp 66The 67.Fn qsort 68and 69.Fn heapsort 70functions sort an array of 71.Fa nmemb 72objects, the initial member of which is pointed to by 73.Fa base . 74The size of each object is specified by 75.Fa size . 76.Fn mergesort 77behaves similarly, but 78.Em requires 79that 80.Fa size 81be greater than 82.Dq "sizeof(void *) / 2" . 83.Pp 84The contents of the array 85.Fa base 86are sorted in ascending order according to 87a comparison function pointed to by 88.Fa compar , 89which requires two arguments pointing to the objects being 90compared. 91.Pp 92The comparison function must return an integer less than, equal to, or 93greater than zero if the first argument is considered to be respectively 94less than, equal to, or greater than the second. 95.Pp 96The functions 97.Fn qsort 98and 99.Fn heapsort 100are 101.Em not 102stable, that is, if two members compare as equal, their order in 103the sorted array is undefined. 104The function 105.Fn mergesort 106is stable. 107.Pp 108The 109.Fn qsort 110function is an implementation of C.A.R. Hoare's 111.Dq quicksort 112algorithm, 113a variant of partition-exchange sorting; in particular, see D.E. Knuth's 114Algorithm Q. 115.Fn qsort 116takes O N lg N average time. 117This implementation uses median selection to avoid its 118O N**2 worst-case behavior. 119.Pp 120The 121.Fn heapsort 122function is an implementation of J.W.J. William's 123.Dq heapsort 124algorithm, 125a variant of selection sorting; in particular, see D.E. Knuth's Algorithm H. 126.Fn heapsort 127takes O N lg N worst-case time. 128Its 129.Em only 130advantage over 131.Fn qsort 132is that it uses almost no additional memory; while 133.Fn qsort 134does not allocate memory, it is implemented using recursion. 135.Pp 136The function 137.Fn mergesort 138requires additional memory of size 139.Fa nmemb * 140.Fa size 141bytes; it should be used only when space is not at a premium. 142.Fn mergesort 143is optimized for data with pre-existing order; its worst case 144time is O N lg N; its best case is O N. 145.Pp 146Normally, 147.Fn qsort 148is faster than 149.Fn mergesort 150is faster than 151.Fn heapsort . 152Memory availability and pre-existing order in the data can make this untrue. 153.Sh RETURN VALUES 154The 155.Fn qsort 156function returns no value. 157.Pp 158Upon successful completion, 159.Fn heapsort 160and 161.Fn mergesort 162return 0. 163Otherwise, they return \-1 and the global variable 164.Va errno 165is set to indicate the error. 166.Sh ERRORS 167The 168.Fn heapsort 169function succeeds unless: 170.Bl -tag -width Er 171.It Bq Er EINVAL 172The 173.Fa size 174argument is zero, or, the 175.Fa size 176argument to 177.Fn mergesort 178is less than 179.Dq "sizeof(void *) / 2" . 180.It Bq Er ENOMEM 181.Fn heapsort 182or 183.Fn mergesort 184were unable to allocate memory. 185.El 186.Sh COMPATIBILITY 187Previous versions of 188.Fn qsort 189did not permit the comparison routine itself to call 190.Fn qsort 3 . 191This is no longer true. 192.Sh SEE ALSO 193.Xr sort 1 , 194.Xr radixsort 3 195.Rs 196.%A Hoare, C.A.R. 197.%D 1962 198.%T "Quicksort" 199.%J "The Computer Journal" 200.%V 5:1 201.%P pp. 10-15 202.Re 203.Rs 204.%A Williams, J.W.J 205.%D 1964 206.%T "Heapsort" 207.%J "Communications of the ACM" 208.%V 7:1 209.%P pp. 347-348 210.Re 211.Rs 212.%A Knuth, D.E. 213.%D 1968 214.%B "The Art of Computer Programming" 215.%V Vol. 3 216.%T "Sorting and Searching" 217.%P pp. 114-123, 145-149 218.Re 219.Rs 220.%A Mcilroy, P.M. 221.%T "Optimistic Sorting and Information Theoretic Complexity" 222.%J "Fourth Annual ACM-SIAM Symposium on Discrete Algorithms" 223.%V January 1992 224.Re 225.Rs 226.%A Bentley, J.L. 227.%T "Engineering a Sort Function" 228.%J "bentley@research.att.com" 229.%V January 1992 230.Re 231.Sh STANDARDS 232The 233.Fn qsort 234function conforms to 235.St -ansiC . 236