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Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_sort_intvec_sort (m01cb)

## Purpose

nag_sort_intvec_sort (m01cb) rearranges a vector of integer numbers into ascending or descending order.

## Syntax

[iv, ifail] = m01cb(iv, m1, order, 'm2', m2)
[iv, ifail] = nag_sort_intvec_sort(iv, m1, order, 'm2', m2)

## Description

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:     $\mathrm{iv}\left({\mathbf{m2}}\right)$int64int32nag_int array
Elements m1 to m2 of iv must contain integer values to be sorted.
2:     $\mathrm{m1}$int64int32nag_int scalar
The index of the first element of iv to be sorted.
Constraint: ${\mathbf{m1}}>0$.
3:     $\mathrm{order}$ – string (length ≥ 1)
If ${\mathbf{order}}=\text{'A'}$, the values will be sorted into ascending (i.e., nondecreasing) order.
If ${\mathbf{order}}=\text{'D'}$, into descending order.
Constraint: ${\mathbf{order}}=\text{'A'}$ or $\text{'D'}$.

### Optional Input Parameters

1:     $\mathrm{m2}$int64int32nag_int scalar
Default: the dimension of the array iv.
The index of the last element of iv to be sorted.
Constraint: ${\mathbf{m2}}\ge {\mathbf{m1}}$.

### Output Parameters

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

## Error Indicators and Warnings

Errors or warnings detected by the function:
${\mathbf{ifail}}=1$
 On entry, ${\mathbf{m2}}<1$, or ${\mathbf{m1}}<1$, or ${\mathbf{m1}}>{\mathbf{m2}}$.
${\mathbf{ifail}}=2$
 On entry, order is not 'A' or 'D'.
${\mathbf{ifail}}=-99$
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.

## Accuracy

Not applicable.

The average time taken by the function is approximately proportional to $n×\mathrm{log}\left(n\right)$, where $n={\mathbf{m2}}-{\mathbf{m1}}+1$. 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.
```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
```