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ALGORITHM 308 GENERATION OF PERMUTATIONS IN PSEUDOLEXICOGRAPHIC ORDER [G6] R. J. ORD-SMIT:H (Recd. 11 Nov. 1966, 1 Dec. 1966, 28 Dee. 1966 and 27 Mar. 1967) Computing Laboratory, University of Bradford, England i f first t h e n b e g i n first := f a l s e ; go t o label e n d ; c o m m e n t the above is the in i t ia l iza t ion process; loop: i f q[k] = k t h e n b e g i n i f k < n t h e n b e g i n k := k + 1; go t o loop e n d e lse begin first := t r u e ; go to f inlsh e n d end; n : = k 1 ; c o m m e n t note n called by value; label: f o r m := 2 s t e p l u n t i l n do q[m] := 1; c o m m e n t af ter the in i t ia l iza t ion the for s t a t e m e n t sets all e lements of q a r ray to 1. Otherwise only the first k--2 elemer~ts are reset 1; q[k] := q[k] + 1; transpose: t := x[l]; x[l] := x[k]; x[k] := t; l : = l + l ; k : = k 1 ; i f l < k t h e n go t o transpose; c o m m e n t when k < 4 only one t ranspos i t ion occurs. On final exit when first is reset t rue , no t ranspos i t ion occurs a t all; ~nish: e n d of procedure ECONOPERM

Remarks on algorithm 87, 102, 130, 202: generation of permutations in lexicographical order