Combination of 1 and 0 in an array in Python
combinations, python, python-2.7, python-itertools
Solution
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.
Problem
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.