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	I	number of items (subset size)
NCAND	I	number of candidates (set size)

GIVEN and RETURNED:

LIST

I(NSEL)

latest combination, LIST(1)=0 to initialize

RETURNED:

J	I	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).