A permutation p₁,p₂,...,p_n of 1,2,...,n is even (resp. odd) 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[1]=p₁, p[2]=p₂, ..., p[n]=p_n 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.

Here's an algorithm that is a little faster than sorting and counting the interchanges:

   I = 1
   SIGNUM = 1
   while I < N
     J = p(I)
     if J = I then
       I = I+1
     else
       SIGNUM = -SIGNUM
       p(I) = p(J)
       p(J) = J
     end if
   end while

Edited on August 5, 2006, 4:15 pm

Posted by Bractals on 2006-08-05 16:14:10