Libraries for ordered combinations generation and ranking? [closed]

Question

I'm looking for a library which could rank/unrank ordered combinations, where ranking means from a combination it give you which nth combinations it is from a Gray code or lexicographic or some other algorithm, unranking is the reversing process.

I look for a library doing many algorithmes like Gray code, lexicographic, rev-lexicographic, enup and so on.

If it does only generation it can be okay if it has many algorithms too.

I found FXT library but it does not use ordered combinations; it does compositions but it seems not to do algorithm of ranking as i need it, it's comparable to rank/unrank unordered combinations.

Answer 1

It's not quite an answer to your question, but there is an excellent book on exactly this topic called Combinatorial Algorithms: Generation, Enumeration, and Search.

It's nicely balanced between the algorithmic/mathematical side and actual implementation. Most of the examples are simple enough that they can be written in a procedural language like C in a very short amount of time.

Answer 2

Do you need something like this:

// get a combination of a rank
// n number k choices N rank

void unrankComb(int* &K, int n, int k, int N)
{
 int e, N2, t, m, p;

 e = nCr(n,k);
 N2 = e-1-N;
 e = ((n - k)*e)/n;
 t = n - k + 1;
 m = k;
 p = n -1;
 do
 {
  if(e <= N2)
  {
   K[k-m] = n - t - m + 2;
   if(e > 0)
   {
    N2 = N2 -e;
    e = (e * m) / p;
   }
   m = m -1;
   p = p -1;
  }
  else
  {
   e = ((p - m)*e) / p;
   t = t - 1;
   p = p - 1;
  }

 }while(m != 0);
}