生成联合分配清单

Question

I'm pretty sure this is an easy problem but I am completely blacking out on how to fix this. I am trying to work my way through the PGM class on coursera and it starts of with joint probability distribution. So I am trying to generate a list of all possible distributions given n variables, where each variable can take on some discrete value between 0...z

so for instance say we have 3 variables, and each can take on values of just 0 and 1 I want to generate this:

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

I am working in python I am drawing a blank on how to dynamically generate this.

Answer 1

If you prefer list comprehension:

[[a, b, c] for a in range(2) for b in range(2) for c in range(2)]

And I forgot to mention that you can use pprint to get the effect you want:

>>> import pprint  
>>> pprint.pprint([[a, b, c] for a in range(2) for b in range(2) for c in range(2)])  
[[0, 0, 0],  
 [0, 0, 1],  
 [0, 1, 0],  
 [0, 1, 1],  
 [1, 0, 0],  
 [1, 0, 1],  
 [1, 1, 0],  
 [1, 1, 1]]  
>>>   

Answer 2

It sounds like you want the Cartesian product:

from itertools import product
for x in product([0,1], [0,1], [0,1]):
    print x

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

Answer 3

Slight improvement over Nathan's method:

>>> import itertools
>>> list(itertools.product([0, 1], repeat=3))
[(0, 0, 0),
 (0, 0, 1),
 (0, 1, 0),
 (0, 1, 1),
 (1, 0, 0),
 (1, 0, 1),
 (1, 1, 0),
 (1, 1, 1)]