php - Is there an algorithm to find unique combinations of 2 lists? 5 lists?

Question

I have N Lists I'd like to find unique combinations of. I've written it out on my whiteboard and it all seems to have a pattern, I just haven't found it yet. I feel I can express a brute-force method and that will certainly be something I pursue. Is there an alternative? Would a different data structure (binary tree?) make a job like this more appropriate?

Given:

#    1  2
a = [1, 2]
b = [a, b]

The result would be:

c = [1a, 1b, 2a, 2b] # (4 unique combinations)

Given:

v = [1, a]
w = [1, b]
x = [1, c]
y = [1, d]
z = [1, e]

The result would be:

r = [11111, 1bcde, 11cde, 111de, 1111e, a1111, ab111, abc11, abcd1, abcde, 1b1d1, 1bc1e, 11c11, 11c1e, ... ] 

Answer 1

Perhaps you are looking for itertools.product:

#!/usr/bin/env python
import itertools
a=[1,2]
b=['a','b']
c=[str(s)+str(t) for s,t in itertools.product(a,b)]
print(c)
['1a', '1b', '2a', '2b']

v=[1,'a']
w=[1,'b']
x=[1,'c']
y=[1,'d']
z=[1,'e']

r=[''.join([str(elt) for elt in p]) for p in itertools.product(v,w,x,y,z)]
print(r)
# ['11111', '1111e', '111d1', '111de', '11c11', '11c1e', '11cd1', '11cde', '1b111', '1b11e', '1b1d1', '1b1de', '1bc11', '1bc1e', '1bcd1', '1bcde', 'a1111', 'a111e', 'a11d1', 'a11de', 'a1c11', 'a1c1e', 'a1cd1', 'a1cde', 'ab111', 'ab11e', 'ab1d1', 'ab1de', 'abc11', 'abc1e', 'abcd1', 'abcde']

Note that product yields 2**5 elements. Is this what you want?

itertools.product is in Python 2.6. For previous versions, you can use this:

def product(*args, **kwds):
        '''
        Source: http://docs.python.org/library/itertools.html#itertools.product
        '''
        # product('ABCD', 'xy') --> Ax Ay Bx By Cx Cy Dx Dy
        # product(range(2), repeat=3) --> 000 001 010 011 100 101 110 111
        pools = map(tuple, args) * kwds.get('repeat', 1)
        result = [[]]
        for pool in pools:
            result = [x+[y] for x in result for y in pool]
        for prod in result:
            yield tuple(prod)

Edit: As jellybean points out, the original question asks for unique sets. The above code will not produce unique sets if a,b,v,w,x,y, or z contain repeated elements. If this is an issue for you, then you can convert each list to a set before sending it to itertools.product:

r=[''.join([str(elt) for elt in p]) for p in itertools.product(*(set(elt) for elt in (v,w,x,y,z)))]