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

Answer 1

I think another answer is in order, to respond to this:

I've written it out on my whiteboard and it all seems to have a pattern, I just haven't found it yet.

There is a pattern.

Suppose you have just two lists to combine. You can find all the combinations by making a grid.

       black        blue
     +------------+------------+
coat | black coat | blue coat  |
     +------------+------------+
hat  | black hat  | blue hat   |
     +------------+------------+

As you can see, there are 2*2 combinations. If there were 30 colors and 14 kinds of clothing, you would have 30 * 14 = 420 combinations.

The pattern continues as you add more lists. Instead of a 2-dimensional rectangle, you get an 3-dimensional array of boxes, or ultimately an n-dimensional hyperrectangle. Regardless, the total number of combinations is always the product of the lengths of all the lists.

If you know how many lists you have, nested loops are a natural way to make all combinations.

for color in colors:
    for kind in kinds:
        print color, kind  # "black coat", "black hat", etc.

If the lists are in dictionary order to start with, and there are no duplicates, the output will also be in dictionary order.