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)

NSEL	I	number of items (subset size)

NCAND	I	number of candidates (set size)

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

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).