All possible combination based on 2^n

I want to create a matrix containing all possible combination. Example of this is shown below. The size of the matrix depends on the number of variable n and the total of combination should follow the . The example below is valid for and, hence, the total number of rows is 8. The value of each element is 0 and 1.

How to create this matrix automatically depending on the number of variable n?

Answer 1

[Stephen23]

n = 3;
m = dec2bin(0:pow2(n)-1)-'0' % limited precision

m = 8×3

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

Or

C = cell(1,n);
[C{:}] = ndgrid(0:1);
C = cellfun(@(a)a(:),C,'uni',0);
M = [C{:}]

M = 8×3

0 0 0 1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1

[BeeTiaw]

It works!

Answer 2

[Dyuman Joshi]

y = flipud(dec2bin(0:2^n-1,n))-'0'  %method 1

y = dec2bin(2^n-1:-1:0,n)-'0'       %method 2

Choose any of the methods you wish, both give the same result.

P.S - There is a similar question in Cody as well.

[Dyuman Joshi]

I see that I am late to the party

[BeeTiaw]

I have another question. Quite similar but the output will be slightly different.

https://uk.mathworks.com/matlabcentral/answers/829783-all-possible-combination-based-on-2-n-but-with-1-and-1

Answer 3

[Stephan]

n = 3

n = 3

ff2n(n)

ans = 8×3

0 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 1 0 1 1 1

[Stephen23]

Note: requires the Statistics and Machine Learning Toolbox.

Answer 4

[Bjorn Gustavsson]

You could use dec2bin:

allpossibles = dec2bin(0:(2^n-1));

You'll have to extract the indices from the columns but that should be "not hard". There's more than likely many prettier solutions, for example have a look on the file exchange for nextperm (by Jos) and next-combination-permutation (by Matt-Fig).

HTH