[Tutor] Automatic generation of an "all possible combinations" array

[Hugh M]

The 2**n different lists that you are seeking have a direct association to
the binary representation of the integers 0 through (2**n)-1.
You can use this fact and the "repeated division method" for converting
numbers between different bases to generate these lists and form the desired
list of lists:

def bit_list_maker(n):
    x = 2**n
    solution_set = []
    for i in range(x):
        this_answer = []
        while i>0:
            this_answer.append(i%2)
            i=i/2
        while len(this_answer)<n:
            this_answer.append(0)
        this_answer.reverse()
        solution_set.append(this_answer)
    return solution_set
*
*
Another fun way to do it is to build up the lists recursively.  The
possibilities for n bits can be built from the possibilities for n-1 bits by
adding a 1 and a 0 to each possibility (ending up with twice as many
elements):

def recursive_bit_list(n):
    if n==1:
        return [[0],[1]]
    else:
        return map(lambda x: x+[0], recursive_bit_list(n-1)) + \
               map(lambda x: x+[1], recursive_bit_list(n-1))

Hope this helps!

-Hugh


On 6/14/07, Andy Cheesman <Andy.cheesman at bristol.ac.uk > wrote:
>
> Hi people
>
> I am trying to generate an array of all possible combinations of 1, and
> zeros (see example data) for a rather nice Kinetic mote Carlo program
> which I am writing python. So far, I've been working out for
> combinations for 4 or less species by hand as it is quick! but I am
> looking to automate the process so I can compute combinations for large
>   numbers of possible species.
> I could automate the generation of the array by the use of multiple
> loops but that doesn't seem rather pythonic. I was wondering if anyone
> had any sensible suggestions or pointers for efficient mechanisms for
> the array.
>
> Many Thanks
> Andy
>
> Example Data
> 3 species
> array([[1, 1, 1],
>        [1, 1, 0],
>        [1, 0, 1],
>        [0, 1, 1],
>        [1, 0, 0],
>        [0, 1, 0],
>        [0, 0, 1],
>        [0, 0, 0]])
> 4 species
> array([[1, 1, 1, 1],
>        [0, 1, 1, 1],
>        [1, 0, 1, 1],
>        [1, 1, 0, 1],
>        [1, 1, 1, 0],
>        [1, 1, 0, 0],
>        [1, 0, 1, 0],
>        [1, 0, 0, 1],
>        [0, 1, 1, 0],
>        [0, 1, 0, 1],
>        [0, 0, 1, 1],
>        [1, 0, 0, 0],
>        [0, 1, 0, 0],
>        [0, 0, 1, 0],
>        [0, 0, 0, 1],
>        [0, 0, 0, 0]])
>
> _______________________________________________
> Tutor maillist  -   Tutor at python.org
> http://mail.python.org/mailman/listinfo/tutor
>
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