Task: Permutations_Rank of a permutation





Java: import java.math.BigInteger;
import java.util.*;

class RankPermutation
{
  public static BigInteger getRank(int[] permutation)
  {
    int n = permutation.length;
    BitSet usedDigits = new BitSet();
    BigInteger rank = BigInteger.ZERO;
    for (int i = 0; i < n; i++)
    {
      rank = rank.multiply(BigInteger.valueOf(n - i));
      int digit = 0;
      int v = -1;
      while ((v = usedDigits.nextClearBit(v + 1)) < permutation[i])
        digit++;
      usedDigits.set(v);
      rank = rank.add(BigInteger.valueOf(digit));
    }
    return rank;
  }
  
  public static int[] getPermutation(int n, BigInteger rank)
  {
    int[] digits = new int[n];
    for (int digit = 2; digit <= n; digit++)
    {
      BigInteger divisor = BigInteger.valueOf(digit);
      digits[n - digit] = rank.mod(divisor).intValue();
      if (digit < n)
        rank = rank.divide(divisor);
    }
    BitSet usedDigits = new BitSet();
    int[] permutation = new int[n];
    for (int i = 0; i < n; i++)
    {
      int v = usedDigits.nextClearBit(0);
      for (int j = 0; j < digits[i]; j++)
        v = usedDigits.nextClearBit(v + 1);
      permutation[i] = v;
      usedDigits.set(v);
    }
    return permutation;
  }
  
  public static void main(String[] args)
  {
    for (int i = 0; i < 6; i++)
    {
      int[] permutation = getPermutation(3, BigInteger.valueOf(i));
      System.out.println(String.valueOf(i) + " --> " + Arrays.toString(permutation) + " --> " + getRank(permutation));
    }
    Random rnd = new Random();
    for (int n : new int[] { 12, 144 })
    {
      BigInteger factorial = BigInteger.ONE;
      for (int i = 2; i <= n; i++)
        factorial = factorial.multiply(BigInteger.valueOf(i));
      
      System.out.println("n = " + n);
      for (int i = 0; i < 5; i++)
      {
        BigInteger rank = new BigInteger((factorial.bitLength() + 1) << 1, rnd);
        rank = rank.mod(factorial);
        int[] permutation = getPermutation(n, rank);
        System.out.println("  " + rank + " --> " + Arrays.toString(permutation) + " --> " + getRank(permutation));
      }
    }
  }
  
}



Python: from math import factorial as fact
from random import randrange
from textwrap import wrap

def identity_perm(n): 
    return list(range(n))

def unranker1(n, r, pi):
    while n > 0:
        n1, (rdivn, rmodn) = n-1, divmod(r, n)
        pi[n1], pi[rmodn] = pi[rmodn], pi[n1]
        n = n1
        r = rdivn
    return pi

def init_pi1(n, pi): 
    pi1 = [-1] * n
    for i in range(n): 
        pi1[pi[i]] = i
    return pi1

def ranker1(n, pi, pi1):
    if n == 1: 
        return 0
    n1 = n-1
    s = pi[n1]
    pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
    pi1[s], pi1[n1] = pi1[n1], pi1[s]
    return s + n * ranker1(n1, pi, pi1)

def unranker2(n, r, pi):
    while n > 0:
        n1 = n-1
        s, rmodf = divmod(r, fact(n1))
        pi[n1], pi[s] = pi[s], pi[n1]
        n = n1
        r = rmodf
    return pi

def ranker2(n, pi, pi1):
    if n == 1: 
        return 0
    n1 = n-1
    s = pi[n1]
    pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
    pi1[s], pi1[n1] = pi1[n1], pi1[s]
    return s * fact(n1) + ranker2(n1, pi, pi1)

def get_random_ranks(permsize, samplesize):    
    perms = fact(permsize)
    ranks = set()
    while len(ranks) < samplesize:
        ranks |= set( randrange(perms) 
                      for r in range(samplesize - len(ranks)) )
    return ranks    

def test1(comment, unranker, ranker):    
    n, samplesize, n2 = 3, 4, 12
    print(comment)
    perms = []
    for r in range(fact(n)):
        pi = identity_perm(n)
        perm = unranker(n, r, pi)
        perms.append((r, perm))
    for r, pi in perms:
        pi1 = init_pi1(n, pi)
        print('  From rank %2i to %r back to %2i' % (r, pi, ranker(n, pi[:], pi1)))
    print('\n  %i random individual samples of %i items:' % (samplesize, n2))
    for r in get_random_ranks(n2, samplesize):
        pi = identity_perm(n2)
        print('    ' + ' '.join('%2i' % i for i in unranker(n2, r, pi)))
    print('')

def test2(comment, unranker):    
    samplesize, n2 = 4, 144
    print(comment)
    print('  %i random individual samples of %i items:' % (samplesize, n2))
    for r in get_random_ranks(n2, samplesize):
        pi = identity_perm(n2)
        print('    ' + '\n      '.join(wrap(repr(unranker(n2, r, pi)))))
    print('')

if __name__ == '__main__':
    test1('First ordering:', unranker1, ranker1)
    test1('Second ordering:', unranker2, ranker2)
    test2('First ordering, large number of perms:', unranker1)