IndexToBinaryState.py

#!/usr/local/bin/python2.7
import math

NUM_DIGITS = 7

def C(m, n):
  if m < n:               return 0
  if m <= 0:              return 0
  if n == 0 or n == m:    return 1
  
  n = min(n, m-n)
  if (m, n) in C.table:   return C.table[(m, n)]
    
  rs = math.factorial(m) / math.factorial(n) / math.factorial(m-n)
  C.table[(m, n)] = rs
  return rs
  

def ConvertIndexToBinaryState(idx, numDigits):
  oneCount = 0
  inGroup = idx
  
  # afther this loop, we can get the values of oneCount and inGroup
  for i in range(numDigits):
    if inGroup >= C(numDigits, i):
      oneCount += 1
      inGroup  -= C(numDigits, i)
    else:
      break
  
  # generate binary string
  s = ""
  for i in range(numDigits-1, -1, -1):
    if oneCount == 0:
      s += '0'
    elif inGroup >= C(i, oneCount):
      s += '1'
      inGroup  -= C(i, oneCount)
      oneCount -= 1
    else:
      s += '0'
  
  return s


C.table = {}  # initial static dictionary variable in function
upperLimit = pow(2, NUM_DIGITS)
for i in range(upperLimit):
  print "%6d => %s" % (i, ConvertIndexToBinaryState(i, NUM_DIGITS))