nag_sort_intvec_sort (m01cb) 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.

References

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

Parameters

Compulsory Input Parameters

1: $iv (m2)$ – int64int32nag_int array: Elements m1 to m2 of iv must contain integer values to be sorted.
2: $m1$ – int64int32nag_int scalar: The index of the first element of iv to be sorted.

Constraint: $m1 > 0$ .
3: $order$ – string (length ≥ 1): If $order ='A'$ , the values will be sorted into ascending (i.e., nondecreasing) order.
If $order ='D'$ , into descending order.

Constraint: $order ='A'$ or $'D'$ .

Optional Input Parameters

1: $m2$ – int64int32nag_int scalar: Default: the dimension of the array iv.
The index of the last element of iv to be sorted.

Constraint: $m2 \geq m1$ .

Output Parameters

1: $iv (m2)$ – int64int32nag_int array: These values are rearranged into sorted order.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,	$m2 < 1$ ,
or	$m1 < 1$ ,
or	$m1 > m2$ .

$ifail = 2$

On entry,

order is not 'A' or 'D'.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

The average time taken by the function is approximately proportional to

n \times \log (n)

, where

n = m2 - m1 + 1

. The worst case time is proportional to

n^{2}

but this is extremely unlikely to occur.

Example

This example reads a list of integers and sorts them into descending order.

Open in the MATLAB editor: m01cb_example

function m01cb_example


fprintf('m01cb example results\n\n');

iv = [int64(23) 45 45 67 69 90 999 1 78 112 24 69 96 99 45 78];
m1 = int64(1);
order = 'Descending';

[iv, ifail] = m01cb(iv, m1, order);

fprintf('Sorted numbers:\n\n');
fprintf('%5d%5d%5d%5d%5d%5d%5d%5d\n',iv);

m01cb example results

Sorted numbers:

  999  112   99   96   90   78   78   69
   69   67   45   45   45   24   23    1

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox