Qsort

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qsort is a C standard library function that implements a sorting algorithm for arrays of arbitrary objects according to a user-provided comparison function. It is named after the "quicker sort" algorithm [1] (a quicksort variant due to R. S. Scowen), which was originally used to implement it in the Unix C library, although the C standard does not require it to implement quicksort. [2]

Contents

The ability to operate on different kinds of data ( polymorphism ) is achieved by taking a function pointer to a three-way comparison function, as well as a parameter that specifies the size of its individual input objects. The C standard requires the comparison function to implement a total order on the items in the input array. [3]

History

A qsort function appears in Version 2 Unix in 1972 as a library assembly language subroutine. Its interface is unlike the modern version, in that it can be pseudo-prototyped as qsort(void * start, void * end, unsigned length) – sorting contiguously-stored length-long byte strings from the range [start, end). [1] This, and the lack of a replaceable comparison function, makes it unsuitable to properly sort the system's little-endian integers, or any other data structures.

In Version 3 Unix, the interface is extended by calling compar(III), with an interface identical to modern-day memcmp. This function may be overridden by the user's program to implement any kind of ordering, in an equivalent fashion to the compar argument to standard qsort (though program-global, of course). [4]

Version 4 Unix adds a C implementation, with an interface equivalent to the standard. [5] It was rewritten in 1983 for the Berkeley Software Distribution. [2] The function was standardized in ANSI C (1989). The assembly implementation is removed in Version 6 Unix. [6]

In 1991, Bell Labs employees observed that AT&T and BSD versions of qsort would consume quadratic time for some simple inputs. Thus Jon Bentley and Douglas McIlroy engineered a new faster and more robust implementation. [2] McIlroy would later produce a more complex quadratic-time input, termed AntiQuicksort, in 1998. This function constructs adversary data on-the-fly. [7]

Example

The following piece of C code shows how to sort a list of integers using qsort.

#include<stdlib.h>/* Comparison function. Receives two generic (void) pointers to the items under comparison. */intcompare_ints(constvoid*p,constvoid*q){intx=*(constint*)p;inty=*(constint*)q;/* Avoid return x - y, which can cause undefined behaviour       because of signed integer overflow. */if(x<y)return-1;// Return -1 if you want ascending, 1 if you want descending order. elseif(x>y)return1;// Return 1 if you want ascending, -1 if you want descending order.return0;// All the logic is often alternatively written:return(x>y)-(x<y);}/* Sort an array of n integers, pointed to by a. */voidsort_ints(int*a,size_tn){qsort(a,n,sizeof(*a),compare_ints);}

Extensions

Since the comparison function of the original qsort only accepts two pointers, passing in additional parameters (e.g. producing a comparison function that compares by the two value's difference with another value) must be done using global variables. The issue was solved by the BSD and GNU Unix-like systems by introducing a qsort_r function, which allows for an additional parameter to be passed to the comparison function. The two versions of qsort_r have different argument orders. C11 Annex K defines a qsort_s essentially identical to GNU's qsort_r. The macOS and FreeBSD libcs also contain qsort_b, a variant that uses blocks, an analogue to closures, as an alternate solution to the same problem. [8]

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References

  1. 1 2 "UNIX Programmer's Manual, Second Edition" (PDF). Bell Telephone Laboratories. June 12, 1972. p. 193. Archived (PDF) from the original on July 30, 2023. Retrieved July 24, 2024– via The Unix Heritage Society.
  2. 1 2 3 Bentley, Jon L.; McIlroy, M. Douglas (1993). "Engineering a sort function". Software: Practice and Experience. 23 (11): 1249–1265. CiteSeerX   10.1.1.14.8162 . doi:10.1002/spe.4380231105. S2CID   8822797. Archived from the original on 2014-01-16. Retrieved 2014-01-14.
  3. ↑ ISO/IEC 9899:201x, Programming Languages—C (draft). §7.22.5. November 16, 2010.
  4. ↑ "UNIX Programmer's Manual, Third Edition". Bell Telephone Laboratories. February 1973. p. qsort(III). Archived from the original on 2023-07-24. Retrieved 2024-07-24– via The Unix Heritage Society.
  5. ↑ "UNIX Programmer's Manual, Fourth Edition". Bell Telephone Laboratories. November 1973. p. qsort(III). Archived from the original on 2023-07-24. Retrieved 2024-07-24– via The Unix Heritage Society.
  6. ↑ "qsort(III), from UNIX Programmer's Manual, Sixth Edition". Unix Archive. Archived from the original on 2023-02-25. Retrieved 2014-09-25.
  7. ↑ McIlroy, M. D. (10 April 1999). "A killer adversary for quicksort" (PDF). Software: Practice and Experience. 29 (4): 341–344. doi:10.1002/(SICI)1097-024X(19990410)29:4<341::AID-SPE237>3.0.CO;2-R. S2CID   35935409. Archived (PDF) from the original on 19 June 2023. Retrieved 24 July 2024.
  8. ↑ qsort_r(3)  –  FreeBSD Library Functions Manual
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