# Creating unique combinations from lists

Reedick, Andrew jr9445 at ATT.COM
Thu Jan 17 15:56:02 CET 2008

```> -----Original Message-----
> From: python-list-bounces+jr9445=att.com at python.org [mailto:python-
> list-bounces+jr9445=att.com at python.org] On Behalf Of Tim Chase
> Sent: Wednesday, January 16, 2008 3:40 PM
> To: breal
> Cc: python-list at python.org
> Subject: Re: Creating unique combinations from lists
>
> You can use a recursive generator:
>
>    def iterall(*iterables):
>      if iterables:
>          for remainder in iterall(*iterables[1:]):
>      else:
>        yield []
>
>    for thing in iterall(
>        ['big', 'medium', 'small'],
>        ['old', 'new'],
>        ['blue', 'green'],
>        ):
>      print thing

Recursion definitely makes for an elegant solution.  However you do take
a bit of a performance hit.  If performance matters (and comprehensions
are supposed to be optimized/fast) and you want a "works for N nested
loops solution," then you could build a N deep comprehension on the fly
and eval() it:

def gen(lists):
out =  '[' + ','.join(["v%s" % i for i in range(len(lists))]) +
']'
comp = ''.join([ " for v%d in lists[%d]" % (i, i) for i in
range(len(lists))])
return eval('[ ' + out + comp + ' ]')

gen([a, b, c])

So for a three item list, it would build and execute the following
comprehension:
[ [v0,v1,v2] for v0 in lists[0] for v1 in lists[1] for v2 in
lists[2] ]
Seven item list:
[ [v0,v1,v2,v3,v4,v5,v6] for v0 in lists[0] for v1 in lists[1]
for v2 in lists[2] for v3 in lists[3] for v4 in lists[4] for v5 in
lists[5] for v6 in lists[6] ]

Some rough performance numbers in seconds for 1,000 iterations over a
three item list:
list comprehension:  0.74
nested for loop   :  0.97  31% slower
recursion         :  3.91 428% slower  =P
eval              :  1.11  50% slower

from timeit import Timer

s = "a = [ i for i in range(10) ]; b = a; c = a"

t = Timer( "l = [ [i, j, k] for i in a for j in b for k in c]", s)

iterations = 1000

print "list comprehension:  %4.2f" % t.timeit(iterations)

t = Timer('''
l = []
for i in a:
for j in b:
for k in c:
l.append([i, j, k])
''', s)

print "nested for loop   :  %4.2f" % t.timeit(iterations)

t = Timer('''
def iterall(*iterables):
if iterables:
for remainder in iterall(*iterables[1:]):
else:
yield []

for thing in iterall(a, b, c):
pass #print thing
''', s)

print "recursion         :  %4.2f" % t.timeit(iterations)

t = Timer('''
def gen(lists):
out =  '[' + ','.join(["v%s" % i for i in range(len(lists))]) +
']'
comp = ''.join([ " for v%d in lists[%d]" % (i, i) for i in
range(len(lists))])
return eval('[ ' + out + comp + ' ]')
gen([a, b, c])
''', s)

print "eval              :  %4.2f" % t.timeit(iterations)

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