NAG Library Function Document

nag_double_sort (m01cac)

nag_double_sort (m01cac) is based on Singleton's implementation of the ‘median-of-three’ Quicksort algorithm, see Singleton (1969), but with two additional modifications. First, small subfiles are sorted by an insertion sort on a separate final pass, see 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[n] – doubleInput/Output: On entry: elements of vec must contain real values to be sorted.

On exit: these values are rearranged into sorted order.
2: n – size_tInput: On entry: the length of vec.
Constraint: $n \geq 1$ .
3: order – Nag_SortOrderInput: On entry: specifies whether the array will be sorted into ascending or descending order.
Constraint: $order = Nag_Ascending$ or $Nag_Descending$ .
4: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, order had an illegal value.
NE_INT_ARG_GT: On entry, $n = ⟨value⟩$ .
Constraint: $n \leq ⟨value⟩$ . This argument is limited by an implementation-dependent size which is printed in the error message.
NE_INT_ARG_LT: On entry, $n = ⟨value⟩$ .
Constraint: $n \geq 1$ .

7 Accuracy

Not applicable.

8 Parallelism and Performance

Not applicable.

9 Further Comments

The average time taken by the function is approximately proportional to

n \log (n)

. The worst case time is proportional to

n^{2}

but this is extremely unlikely to occur.

10 Example

The example program reads a list of real numbers and sorts them into ascending order.

NAG Library Function Documentnag_double_sort (m01cac)

+− Contents

1 Purpose

2 Specification

3 Description