SLA_COMBN - Next Combination   

ACTION:

Generate the next combination, a subset of a specified size chosen from a specified number of items.

CALL:

CALL sla_COMBN (NSEL, NCAND, LIST, J)

GIVEN:

NSEL number of items (subset size)

NCAND I number of candidates (set size)

GIVEN and RETURNED:

LIST latest combination, LIST(1)=0 to initialize

RETURNED:

J status: -1 = illegal NSEL or NCAND 0 = OK +1 = no more combinations available

NOTES:

1.

NSEL and NCAND must both be at least 1, and NSEL must be less than or equal to NCAND.

2.

This routine returns, in the LIST array, a subset of NSEL integers chosen from the range 1 to NCAND inclusive, in ascending order. Before calling the routine for the first time, the caller must set the first element of the LIST array to zero (any value less than 1 will do) to cause initialization.

3.

The first combination to be generated is:

LIST(1)=1, LIST(2)=2, ..., LIST(NSEL)=NSEL

This is also the combination returned for the ``finished'' (J=1) case. The final permutation to be generated is:

LIST(1)=NCAND, LIST(2)=NCAND-1, ...,
                               LIST(NSEL)=NCAND-NSEL+1

4.

If the ``finished'' (J=1) status is ignored, the routine continues to deliver combinations, the pattern repeating every NCAND!/(NSEL!(NCAND-NSEL)!) calls.

5.

The algorithm is by R.F.Warren-Smith (private communication).