Combination of 1 and 0 in an array in Python

Question

I want to make a combination of 1's and 0's in a 2d array like the following:

[[ 1, 1, 1, 1, 0, 0, 0, 0 ],
 [ 1, 1, 1, 0, 1, 0, 0, 0 ],
 [ 1, 1, 1, 0, 0, 1, 0, 0 ],
 [ 1, 1, 1, 0, 0, 0, 1, 0 ],
 [ 1, 1, 1, 0, 0, 0, 0, 1 ],
 .
 .
 .
]

That means a combination of four 1's and four 0's. I have looked at the itertools module's permutations() and combinations(), but couldn't find any suitable functions to perform this combination.

Answer 1

You can also use combinations to generate unique combinations directly:

n = 8
n1 = 4
for x in itertools.combinations( xrange(n), n1 ) :
    print [ 1 if i in x else 0 for i in xrange(n) ] 

[1, 1, 1, 1, 0, 0, 0, 0]
[1, 1, 1, 0, 1, 0, 0, 0]
[1, 1, 1, 0, 0, 1, 0, 0]
[1, 1, 1, 0, 0, 0, 1, 0]
...
[0, 0, 0, 1, 1, 1, 0, 1]
[0, 0, 0, 1, 1, 0, 1, 1]
[0, 0, 0, 1, 0, 1, 1, 1]
[0, 0, 0, 0, 1, 1, 1, 1]

This is more efficient than permutations because you don't iterate over unwanted solutions.

The intuition is that you're trying to find all possible ways to fit four "1"s in a sequence of length 8; that's the exact definition of combinations. That number is C(8,4)=8! / (4! * 4!) = 70. In contrast, the solution using permutations iterates over 8! = 40,320 candidate solutions.