A079885 Number of index tests required to create all permutations of n distinct elements using the "streamlined" version of Algorithm L (lexicographic permutation generation) from Knuth's The Art of Computer Programming, Vol. 4, chapter 7.2.1.2.

0, 4, 29, 185, 1314, 10534, 94839, 948427, 10432748, 125193032, 1627509489, 22785132925

Offset: 3

Author

Hugo Pfoertner, Jan 13 2003

Keywords

• nonn

Comments

The required number of index tests (test for termination and test in the final reversion loop) becomes 0.2613625*n! for large n, if the test for n=3 is excluded. If n=3 is included the additionally required termination test adds n!/6 index comparisons, increasing the number of index comparisons to 0.428029*n! (63.8% more index comparisons).

The corresponding number of index tests needed by the "pure" Algorithm L is given by A038156(n)+A080048(n), which is 12.478..*a(n) for large n.

References

• For references and corresponding links see under A079884

Links

• Hugo Pfoertner, FORTRAN program for lexicographic permutation generation.

Crossrefs

Cf. A000142, partial counts given in A079751, A079755. Number of element comparisons: A079884.

Cf. A038156, A080048.

Programs

Fortran

! program available at link

Formula

a(3)=0, a(n)=n*a(n-1)+1+(n-1)*floor((n-1)/2) for n>=4 a(n) = A079751(n) + A079755(n)

For n>=3 a(n)=floor(c*n!-(n-3)/2) where c=limit n-->infinity a(n)/n!= 0.261362463274289013838... - Benoit Cloitre, Jan 20 2003

In closed form, c = 3*exp(1)/2 + exp(-1)/2 - 4. - Vaclav Kotesovec, Mar 18 2014