NAG Library Routine Document

M01CCF

M01CCF 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.

Only the substring (L1:L2) of each element of the array CH is used to determine the sorted order, but the entire elements are rearranged into sorted order.

4 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

5 Parameters

1: CH(M2) – CHARACTER(*) arrayInput/Output: On entry: elements M1 to M2 of CH must contain character data to be sorted.
Constraint: the length of each element of CH must not exceed $255$ .

On exit: these values are rearranged into sorted order.
2: M1 – INTEGERInput: On entry: the index of the first element of CH to be sorted.
Constraint: $M1 > 0$ .
3: M2 – INTEGERInput: On entry: the index of the last element of CH to be sorted.
Constraint: $M2 \geq M1$ .
4: L1 – INTEGERInput
5: L2 – INTEGERInput: On entry: only the substring (L1:L2) of each element of CH is to be used in determining the sorted order.
Constraint: $0 < L1 \leq L2 \leq LEN (CH (1))$ .
6: ORDER – CHARACTER(1)Input: On entry: if $ORDER ='A'$ , the values will be sorted into ASCII order.
If $ORDER ='R'$ , into reverse ASCII order.

Constraint: $ORDER ='A'$ or $'R'$ .
7: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,	$M2 < 1$ ,
or	$M1 < 1$ ,
or	$M1 > M2$ ,
or	$L2 < 1$ ,
or	$L1 < 1$ ,
or	$L1 > L2$ ,
or	$L2 > LEN (CH (1))$ .

$IFAIL = 2$

On entry,

ORDER is not 'A' or 'R'.

$IFAIL = 3$

On entry,

the length of each element of CH exceeds

255

7 Accuracy

Not applicable.

8 Further Comments

The average time taken by the routine 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.

The routine relies on the Fortran intrinsic functions LLT and LGT to order characters according to the ASCII collating sequence.

9 Example

This example reads a file of

12

-character records, and sorts them into reverse ASCII order on characters

7

12

NAG Library Routine DocumentM01CCF

+− Contents

1 Purpose

2 Specification

3 Description