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# Matrix with all possibilities

Asked by Rik on 28 Dec 2012

Dear all,

I would like to create a matrix with all possibilities, such as the following: [1 1 1; 1 1 0; 1 0 1; 0 1 1; 1 0 0; 0 1 0; 0 0 1; 0 0 0]

I have tried to use nchoosek([0 0 0 1 1 1],3) but this function fails in ordering. Furthermore I tried C = npermutek([ones(1,3) zeros(1,3)],3); D = unique(C,'rows'), but this one gives a out of memory error for larger vectors (8 instead of 3). For this function see: http://www.mathworks.com/matlabcentral/fileexchange/11462-npermutek/

How to create such a matrix?

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Answer by Jan Simon on 28 Dec 2012

Searching the FileExchange for the terms "combinations" and "permutations" helps to find:

Answer by Azzi Abdelmalek on 28 Dec 2012
Edited by Azzi Abdelmalek on 28 Dec 2012
```out=[]
n=3
for k=1:n
s=[ones(2^(n-k ),1) ;zeros(2^(n-k ),1)]
s=repmat(s,2^(k-1),1)
out=[out s]
end
```

Answer by Roger Stafford on 29 Dec 2012

Here is a variation on Azzi's solution:

``` A = ones(2^n,n);
p = 1;
for k = 0:n-1
A(p+1:2*p,n-k:n) = [zeros(p,1),A(1:p,n-k+1:n)];
p = 2*p;
end```

To count up instead of down, swap the 'ones' and 'zeros' calls.