Comma Free Dictionaries | Python Fiddle

# To use, change the values of n and k below to whatever you want, 
# then press the run button in the upper left hand corner.

n = 2
k = 9

def comma_free_dict(n, k):
    """Only guaranteed to work when k is odd"""
    # Maintain a list of lists of the words found in each stage.
    stages = [] 
    current_stage = map(str,range(n)) # First stage is [0, 1, ..., n-1]
    while len(current_stage) > 0: # Keep going until the stage created is empty
        current_stage = next_stage(current_stage,k)
        stages.append(current_stage)
    # Finally, lump all the stages together, and
    # only keep the words whose length is the length we want
    return [w for w in sum(stages,[]) if len(w) == k]

def next_stage(prev_stage,word_length):
    """
    Given list of words in S_n, and the desired length of words in the dictionary,
    returns the list of words in S_{n+1}.
    """
    # Find all odd length words, sorted by length
    odd_words = [w for (l,w) in sorted([(len(w),w) for w in prev_stage if len(w)%2 == 1])]
    if len(odd_words)==0:
        # If there aren't any odd words, we are done, so return the empty list
        return [] 
    # Otherwise, the prefix we use the shortest odd word.
    prefix = odd_words[0] 
    # Remove any words which are already long enough
    prev_stage = [w for w in prev_stage if len(w)<word_length]
    # Take all remaining words (except the prefix), and
    # place the prefix in front of them as many times as possible.
    # The sum(,[]) part takes all the lists given by expand, and concatenates them together
    return sum([expand(prefix,word,word_length) for word in prev_stage if word != prefix],[])

def expand(prefix, word, max_length):
    """Put the string 'prefix' in front of the string 'word' as many times as possible,
        without exceeding max_length. Returns a list of all such words.
    """
    words = []
    current = word
    while len(current)<= max_length:
        words.append(current)
        current = prefix + current
    return words

dictionary = sorted(comma_free_dict(n,k))[::-1]
line = ''
while dictionary:
    if len(line)<80:
        line += dictionary.pop() + '   '
    else:
        print line
        line = ''
print line

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