Python generate all possible combinations of matrix

问题

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.

回答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

回答2:

If you want all matrices at once, just produce flat lists using itertools.product and numpy.reshape them:

from itertools import product
import numpy as np

n, m = 2, 2

x = product([1, 0], repeat=n*m)
x = np.reshape(list(x), (-1, n, m))
print(x)

With the output for 2x2:

array([[[1, 1],
        [1, 1]],

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

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

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

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

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

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

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

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

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

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

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

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

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

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

       [[0, 0],
        [0, 0]]])

Note that for n, m = 16, 16 there are 2**(16*16) combinations, which is about 10**77, so much too large to fit into memory. In that case you probably have to process each matrix on its own:

def get_combinations(n, m):
    for flat in product([1, 0], repeat=n*m):
        yield np.reshape(flat, (n, m))

Which you can use like this:

from itertools import islice

for m in islice(get_combinations(3, 3), 3):  # only get the first three
    print(m)

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

来源：https://stackoverflow.com/questions/54923928/python-generate-all-possible-combinations-of-matrix

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python

list

math

combinations