Compute rank of a combination?

Question

I want to pre-compute some values for each combination in a set of combinations. For example, when choosing 3 numbers from 0 to 12, I\'ll compute some value for each one:

Answer 1

What you want are called combinadics. Here's my implementation of this concept, in Python:

def nthresh(k, idx):
  """Finds the largest value m such that C(m, k) <= idx."""
  mk = k
  while ncombs(mk, k) <= idx:
    mk += 1
  return mk - 1


def idx_to_set(k, idx):
  ret = []
  for i in range(k, 0, -1):
    element = nthresh(i, idx)
    ret.append(element)
    idx -= ncombs(element, i)
  return ret


def set_to_idx(input):
  ret = 0
  for k, ck in enumerate(sorted(input)):
    ret += ncombs(ck, k + 1)
  return ret