Generating all combinations

[pataphor]

Johannes Bauer wrote:

> Any help is appreciated!

This is on the fringe of exploitation, but hey, maybe the code helps you 
think about the algorithm.

IMHO the following code is a glaring complaint about the injustice of 
omission itertools inflicts on the perfectly natural and obvious 
procedure of repeat_each (whatever it's name ought to be):

from itertools  import izip, islice, cycle

def repeat_each(seq,n):
     while True:
         for x in seq:
             for i in range(n):
                 yield x

def repeat_all(seq,n):
     while True:
         for i in range(n):
             for x in seq:
                 yield x

def product(X):
     N = []
     total = 1
     for x in X:
         N.append(total)
         total *= len(x)
     R = [repeat_all(repeat_each(x,k),n)
                     for x,k,n in izip(X,N,reversed(N))]
     return islice(izip(*R),total)

def test1():
     L = ['a', 'bc','def' ]
     for x in product(L):
         print x
     print

def test2():
     repeat_all = cycle
     test1()

if __name__ == '__main__':
     test1()
     test2()

See? Repeat_all and repeat_each are almost brothers, just separated by 
the tiniest rearrangement of their genetic code (or should I say code 
genetics?). Yet one is included as 'itertools.cycle' and the other is 
doomed to live in limbo. Such injustice! Can it be that 
'itertools.repeat' has usurped repeat_each's rightful position?

P.