How to create this list?

Questions
,
1

Hello,
I am new to Mathematica and I want to create the following list.
Suppose that each entry of a N-dimensional vector can be 0 or 1. How do I obtain all possible N-dimensional vectors where each entry could be 0 or 1?
I was able to write the following code but it only works for small N.

l[1] = {0, 1};
l[n_] := l[n] = Flatten[{0, 1, l[n - 1]}, n]
A[n_] := DeleteDuplicates[Subsets[Flatten[{l[n], l[n]}], {n}]]
A[2]
(*{{0, 1}, {0, 0}, {1, 0}, {1, 1}}*)

Kind regards

2

Hi,

try

Tuples[{0, 1}, 2]
(*{{0, 0}, {0, 1}, {1, 0}, {1, 1}}*)

If you change 2 to any N, it should do what you want.

Cheers,

M.

3

Hi Marco,
Thank you so much for your reply. I was not aware of this function.
Many thanks again.

4

I just notice that even Tuples breaks down for large N. If we take N = 100, we have the following error

Tuples::toomany: The length of the output of Tuples[{0,1},100] should be a machine integer. >>

Is there a way to go around it?

5

Hi,

I don’t think that N=100 is feasible. There are 2^{100} different tuples of dimension 100 consisting of entries one and zero. That’s a rather large number.

2^100

(*1267650600228229401496703205376*)

That is a huge number. One entry such as \{0,0\} requires 88 Bytes.

ByteCount[{0, 0}]
(*88*)

If we multiply that by 2^{100} we get a really large number. Rough estimate (might be wrong) is that you need about 10^{19} 1 TB hard drives to store that amount of data.

Even lower dimensions like N=30 cause problems.

Best wishes,

Marco

6

Hi,

BTW see also this discussion:

http://mathematica.stackexchange.com/questions/46304/generate-a-list-of-values-with-equal-number-of-each-value

The $MaxMachineInteger on my computer is:

Developer`$MaxMachineInteger
(*9223372036854775807*)

which corresponds to

Log[2, Developer`$MaxMachineInteger] // N
(*63.*)

Notably,

Tuples[{0,1},63]
(*Tuples::toomany: The length of the output of Tuples[{0,1},63] should be a machine integer. >>*)

Tuples[{0,1},62]
(*General::nomem: The current computation was aborted because there was insufficient memory available to complete the computation.*)

So there is a system issue, i.e. address the array, and also there is a memory issue.

Cheers,

M.