m01 Chapter Contents
m01 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_quicksort (m01csc)

## 1  Purpose

nag_quicksort (m01csc) rearranges a vector of arbitrary type objects into ascending or descending order.

## 2  Specification

 #include #include
void  nag_quicksort (Pointer vec, size_t n, size_t size, ptrdiff_t stride,
 Integer (*compare)(const Nag_Pointer a, const Nag_Pointer b),
Nag_SortOrder order, NagError *fail)

## 3  Description

nag_quicksort (m01csc) sorts a set of $n$ data objects of arbitrary type, which are stored in the elements of an array at intervals of length stride. The function may be used to sort a column of a two-dimensional array. Either ascending or descending sort order may be specified.
nag_quicksort (m01csc) is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm, Singleton (1969), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass, Sedgewick (1978). Second, if a subfile is partitioned into two very unbalanced subfiles, the larger of them is flagged for special treatment: before it is partitioned, its end-points are swapped with two random points within it; this makes the worst case behaviour extremely unlikely.

## 4  References

Maclaren N M (1985) Comput. J. 28 448
Sedgewick R (1978) Implementing Quicksort programs Comm. ACM 21 847–857
Singleton R C (1969) An efficient algorithm for sorting with minimal storage: Algorithm 347 Comm. ACM 12 185–187

## 5  Arguments

1:     vec[${\mathbf{n}}$]Pointer Input/Output
On entry: the array of objects to be sorted.
On exit: the objects rearranged into sorted order.
2:     nsize_tInput
On entry: the number, $n$, of objects to be sorted.
Constraint: ${\mathbf{n}}\ge 0$.
3:     sizesize_tInput
On entry: the size of each object to be sorted.
Constraint: ${\mathbf{size}}\ge 1$.
4:     strideptrdiff_tInput
On entry: the increment between data items in vec to be sorted.
Note: if stride is positive, vec should point at the first data object; otherwise vec should point at the last data object.
Constraint: $\left|{\mathbf{stride}}\right|\ge {\mathbf{size}}$.
5:     comparefunction, supplied by the userExternal Function
nag_quicksort (m01csc) compares two data objects. If its arguments are pointers to a structure, this function must allow for the offset of the data field in the structure (if it is not the first).
The function must return:
 $-1$ if the first data field is less than the second, $\phantom{-}0$ if the first data field is equal to the second, $\phantom{-}1$ if the first data field is greater than the second.
The specification of compare is:
 Integer compare (const Nag_Pointer a, const Nag_Pointer b)
1:     aconst Nag_Pointer Input
On entry: the first data field.
2:     bconst Nag_Pointer Input
On entry: the second data field.
6:     orderNag_SortOrderInput
On entry: specifies whether the array is to be sorted into ascending or descending order.
Constraint: ${\mathbf{order}}=\mathrm{Nag_Ascending}$ or $\mathrm{Nag_Descending}$.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_2_INT_ARG_LT
On entry, $\left|{\mathbf{stride}}\right|=〈\mathit{\text{value}}〉$ while ${\mathbf{size}}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\left|{\mathbf{stride}}\right|\ge {\mathbf{size}}$.
NE_ALLOC_FAIL
Dynamic memory allocation failed.
On entry, argument order had an illegal value.
NE_INT_ARG_GT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\le 〈\mathit{\text{value}}〉$.
On entry, ${\mathbf{size}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{size}}\le 〈\mathit{\text{value}}〉$.
These arguments are limited to an implementation-dependent size which is printed in the error message.
NE_INT_ARG_LT
On entry, ${\mathbf{n}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{n}}\ge 0$.
On entry, ${\mathbf{size}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{size}}\ge 1$.
The absolute value of stride must not be less than size.

## 7  Accuracy

Not applicable.

The average time taken by the function is approximately proportional to $n\mathrm{log}n$. The worst case time is proportional to ${n}^{2}$ but this is extremely unlikely to occur.

## 9  Example

The example program reads a two-dimensional array of numbers and sorts the second column into ascending order.

### 9.1  Program Text

Program Text (m01csce.c)

### 9.2  Program Data

Program Data (m01csce.d)

### 9.3  Program Results

Program Results (m01csce.r)