Generating all binary combinations of 2d array in Python

Question

I am trying to generate all possible 2D arrays (of size n*n) of 0 and 1. Since there are two choices for each entry of the 2D array, there are 2^{n^2} such arrays that need to be generated.

I have a code that generates all possible 1D arrays (of size n) of 0 and 1. It is:

def generateAllSpinConfigs(n,arr,l,i):
    if i == n: 
        l.append(arr[:]) 
        return

    arr[i] = 0
    generateAllSpinConfigs(n,arr,l,i+1)  
    arr[i] = 1
    generateAllSpinConfigs(n,arr,l,i+1)  

    return l

arr=[None]*n 
l=[]
answer=generateAllSpinConfigs(n,arr,l,0)

I understand how that works. In this recursive code, the lowest function call returns an array of all 0 first, then an array with all 0 with a 1 in the last location and so on. Can we extend this logic to generate all 2D arrays or is there a Python function that does the job that I'm not aware of?

Consider that a binary array can be seen a number. A 2D array of dimension (x, y) has x * y = n bits. The number of combination is 2^n or 2^(x*y). So, for example, an 4x4 array would be 2^16 = 65535 combinations. A 6x6 is would have 68719476736 combination, larger than what can fit in an int. It quickly gets out of hand. — Ouroborus
– Ouroborus, Commented Jul 22, 2022 at 19:40
@Ouroborus True, it increases exponentially. Thanks, I am aware of itertools.combinations but it doesn't have an option for a 2D array? — q2w3e4
– q2w3e4, Commented Jul 22, 2022 at 19:41
A x*y 2d array is the same as a n-length 1d array, where x*y = n. Generate the 1d array, then reshape it to 2d. — Ouroborus
– Ouroborus, Commented Jul 22, 2022 at 19:45

trincot · Accepted Answer · 2022-07-22 19:59:08Z

1

You can use itertools.product. First to generate 1-dimensional lists, and then again to use that as a basis to increase the dimension:

from itertools import product

def get_bin_rows(size):
    return product(range(2), repeat=size)

def get_bin_matrices(size):
    return product(get_bin_rows(size), repeat=size)

Example use for n=2:

for matrix in get_bin_matrices(2):
    # print matrix row by row
    for row in matrix:
        print(*row)
    print()  # separate matrix outputs

answered Jul 22, 2022 at 19:59

trincot

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