[R] sign(<permutation>) in R ?

[Martin Maechler]

I am looking for an algorithm (written in R (preferably) or C,
but even pseudo-code in a text book maybe fine)
to determine the sign of a permutation.

What is that?  Well, a permutation is either even or odd, the
sign is +1 or -1, respectively, see, e.g.,
   http://en.wikipedia.org/wiki/Signature_of_a_permutation
which also says
 >> In practice, in order to determine whether a given permutation
 >> is even or odd, one writes the permutation as a product of
 >> disjoint cycles. The permutation is odd if and only if this
 >> factorization contains an odd number of even-length cycles.

but I would not know how to algorithmically
  "write the permutation as a product of disjoint cycles"

If you start looking at R code, 
let's assume the permutation {\pi(i)}_{i=1..n} is simply given
as the (integer) vector (\pi(1), \pi(2), ..., \pi(n))
{or equivalently, a random permutation is simply found by  'sample(n)'}

Thank you in advance for further pointers,
or even working R code.

Best regards,
Martin Maechler, ETH Zurich