recursion - Trying to write a python recursive function -

i have following list:

list = ['abc', 'def', 'ghi'] 

what best way write recursive function pick 1 letter each group of 3 , return possible combinations/permutations:

e.g. output follows:

a, ad, adg, adh, adi, aeg, aeh, aei, afg, afh, afi

b, bd, bdg, bdh, bdi, beg, beh, bei, bfg, bfh, bfi

c, cd, cdg, cdh, cdi, ceg, ceh, cei, cfg, cfh, cfi

d, dg, dga, dgb, dgc, dha, ... , on ...

i'm learning recursive functions. have spend 7 straight hours on problem far , still near. appreciated!

consider empty list, result empty list (this 'base case'), i.e.

f([]) == "" 

for non-empty list, take each character of first list element (the 'head' of list) , prepend each string returned recursively applying function remainder (the 'tail') of list (this 'recursive case'):

f(['abc'])   == 'a' + f([]), 'b' + f([]), 'c' + f([])   == 'a' + '', 'b' + '', 'c' + ''   == 'a', 'b', 'c'  f(['abc', def'])   == 'a' + f(['def']), 'b' + f(['def']), 'c' + f(['def'])   == 'a' + 'd' + f([]), 'a' + 'e' + f([]), 'a' + 'f' + f([]), 'b' + 'd' + f([]) ...   == 'ad', 'ae', 'af', 'bd', 'be', 'bf', 'cd', 'ce', 'cf' 

in python, expressed (somewhat inefficient , verbose, point show algorithm):

def f(xs):     if not xs:         yield ''     else:         head = xs[0]         tail = xs[1:]          char in head:             yield char             s in f(tail):                 yield char + s 

calling function like

print list(f(['abc', 'def', 'ghi'])) 

prints

['a', 'ad', 'adg', 'adg', 'adh', 'adh', 'adi', 'adi', 'ae', 'aeg', 'aeg', 'aeh', 'aeh', 'aei', 'aei', 'af', 'afg', 'afg', 'afh', 'afh', 'afi', 'afi', 'b', 'bd', 'bdg', 'bdg', 'bdh', 'bdh', 'bdi', 'bdi', 'be', 'beg', 'beg', 'beh', 'beh', 'bei', 'bei', 'bf', 'bfg', 'bfg', 'bfh', 'bfh', 'bfi', 'bfi', 'c', 'cd', 'cdg', 'cdg', 'cdh', 'cdh', 'cdi', 'cdi', 'ce', 'ceg', 'ceg', 'ceh', 'ceh', 'cei', 'cei', 'cf', 'cfg', 'cfg', 'cfh', 'cfh', 'cfi', 'cfi']