Python generate all possible combinations of matrix

Question

I need to generate all combinations of a matrix in Python. The input will be two integers n and m, and I need to generate all possible states of that matrix with 1 and 0 as possible values.

For example:

n = 3 m = 2
[[0 0 0] [1 0 0] [1 1 0]
 [0 0 0] [0 0 0] [0 0 0]
 [0 0 0],[0 0 0],[0 0 0] . . . . .
]

Is there a clean and efficient way to do this given I will not know the values for n and m until runtime? The highest value used will be n = 16 m = 16.

Answer 1

One way is by generating all binary sequences of length m*n in a list comprehension, and reshaping them into a (m,n) shaped nested list on each iteration.

A simple way to generate all sequences is by taking the cartesian product of 01 with n*m repeats, which will be produce 2^(m*n) combinations:

from itertools import product
m=3
n=3

x = [[list(i[x:x+m]) for x in range(0, len(i), m)] for i in product("01", repeat=m*n)]

Output

[[['0' '0' '0']
  ['0' '0' '0']
  ['0' '0' '0']]

 [['0' '0' '0']
  ['0' '0' '0']
  ['0' '0' '1']]

 [['0' '0' '0']
  ['0' '0' '0']
  ['0' '1' '0']]
 ...

print(len(x))
# 512