Groups anagrams in lists (without sorting)

anagram_grouper.py

#!/usr/bin/python

from prime_number_generator import prime_number_generator
from operator import mul
from string import lowercase

P_GEN = prime_number_generator()
REF = { elem : P_GEN.next() for elem in lowercase }

def anagram_grouper(input_list):
    '''
    Groups anagrams in lists.

    Time complexity : O(n*k) where n is size of 'input_list' and
    k is the length of longest word.
    '''
    final = {}
    for elem in input_list:
        char_prod = reduce(mul, [REF[char] for char in elem.lower()])
        final[char_prod] = final.get(char_prod, []) + [elem]
    for key in final:
        print final[key]

if __name__ == '__main__':
    anagram_grouper(['abc', 'asfsadad', 'bcs', 'bca'])