🚀 go-pugleaf

Aaargh.  Somehow, in my effort to get the permutation algorithm
from my head to a clear written explanation, I managed to flub 
at least two key points.  Prof. Meyerson points out both of them:

In article <2607@usna.NAVY.MIL> mdm@math3.sma.usna.navy.mil (Mark D. Meyerson -- math  FACULTY <mdm@sma.usna.navy.mil>) writes:
>This method fails.  There is a minor error in that letting
>p=0 and using modular arithmetic gives zero values outside
>of the subscript range of the arrays.  This is easily 
>patched.

True.  I should have indexed both arrays v and w from 0 to N-1 in the
first place, and initialized t to N-1 as well.  I hope this fixes this
error.

>  But a major error is that  k mod b  won't 
>distinguish between different k.  The first example of this
>failure is for N=4 and k=4 or 16 (N!=24 so both k values occur.)

This is really the major omission from the algorithm.  I had meant
to compute both k mod b *and* k div b.  k mod b is used to index the
array for the current selection; k div b is then copied to k for the
next round.

With the division step properly included in the algorithm, the
resulting permutations for k=4 and k=16 are 1,4,3,2 and 1,2,4,3
respectively.  If you get different results then most likely I have
made some other error in the description of the algorithm.

Actually I suspect my algorithm may be fundamentally the same as
another one that was posted that was supposedly based on FORTRAN
multidimensional array indexing, but I came down with a bad case of
MEGO when I looked at the FORTRAN code so I can't say for sure.

-- David Karr (karr@cs.cornell.edu)