How to create a cartesian product excluding some results?

Question

For my calculations, I need all 32-element cartesian products composed of 0 and 1, where there is twelve 1.

I'm currently using the following method:

for k,l in enumerate(itertools.product([0,1], repeat=32)):
        if l.count(1)==12:                                        
            # rest code

But as you can see, it is not very optimal for such a large cartesian product.

How build the list that I need without having to go through all the elements itertools.product and without an additional if condition? Is there a faster way to do this?

Answer 1

This will only generate lists of bits elements where ones are 1 and the rest are 0:

def binLimit1s( bits, ones, prefix=[] ):
    if bits<ones:
        yield prefix
    elif ones==0:
        yield prefix + [0]*bits
    elif ones==bits:
        yield prefix + [1]*bits
    else:
        for x in binLimit1s( bits-1, ones, prefix+[0] ):
            yield x
        for x in binLimit1s( bits-1, ones-1, prefix+[1] ):
            yield x

For example,

>>> list(binLimit1s(4, 3))
[[0, 1, 1, 1], [1, 0, 1, 1], [1, 1, 0, 1], [1, 1, 1, 0]]

In your case, you would use

binLimit1s( 32, 12 )