Ranking and unranking of permutations with duplicates

Question

I\'m reading about permutations and I\'m interested in ranking/unranking methods.

From the abstract of a paper:

A ranking function for the per

Answer 1

Java, from https://github.com/timtiemens/permute/blob/master/src/main/java/permute/PermuteUtil.java (my public domain code, minus the error checking):

public class PermuteUtil {
 public  List nthPermutation(List original, final BigInteger permutationNumber)  {
        final int size = original.size();

        // the return list:
        List ret = new ArrayList<>();
        // local mutable copy of the original list:
        List numbers = new ArrayList<>(original);

        // Our input permutationNumber is [1,N!], but array indexes are [0,N!-1], so subtract one:
        BigInteger permNum = permutationNumber.subtract(BigInteger.ONE);

        for (int i = 1; i <= size; i++) {
            BigInteger factorialNminusI = factorial(size - i);

            // casting to integer is ok here, because even though permNum _could_ be big,
            //   the factorialNminusI is _always_ big
            int j = permNum.divide(factorialNminusI).intValue();

            permNum = permNum.mod(factorialNminusI);

            // remove item at index j, and put it in the return list at the end
            T item = numbers.remove(j);
            ret.add(item);
        }

        return ret;
  }
}