A permutation p1
of 1,2,...,n is even
) if it can be returned to the original order 1,2,...,n using an even (resp. odd) number of interchanges of pairs of elements. It is known that every permutation is either even or odd (and therefore not both).
The sign, or signum (for those who want to be fancy), of a permutation is +1 for an even permutation and -1 for an odd permutation.
You are given the integer n and the array p initialized to the integer values p=p1, p=p2, ..., p[n]=pn which are guaranteed to be a permutation of 1,2,...,n. What algorithm would you advocate for determining the sign of the permutation? You need not preserve the original contents of p.
(In reply to re(2): No Subject
4321 and 4312 have opposite
sign, of course, as do 2143=(12)(34) and 4123=(1234), where I have also
expressed the latter two in cycle notation which makes their parities
Posted by Richard
on 2006-08-07 14:14:05