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# how to write code to try every combination of N-dim vector?

Asked by C Zeng on 22 May 2012

Hello, I want to write a code to try every combination of a N-dimentional vector(with entry 0 or 1 or 2). For example, if N=3, all combinations are (0,0,0)(0,0,1)...(2,2,2) and there are 3^N=27.

One brutal way is for commands: for i=0:2->for j=... but I have to write N these for commands, which is not wise. I wonder it there a fast and smart way to try all combinations?

Thanks a lot!

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Answer by Sean de Wolski on 22 May 2012
```[xx yy zz] = ndgrid(0:2);
[xx(:) yy(:) zz(:)]
```

Generalized (fixed)

```n = 4
[C{1:n}] = ndgrid(0:2);
for ii = n:-1:1
M(:,ii) = C{ii}(:);
end
```

C Zeng on 22 May 2012

Can I write like this:
For i=1 to 3^N
[a1,a2,a3,a4]=M(i,:);
then define function and solve the value;
compare and find the maximizer;
end;

It works well I think.

C Zeng on 24 May 2012

Hi, the code does not work and try all combinations:
n = 4
[C{1:n}] = ndgrid(0:2);
reshape(vertcat(C{:}),[],n)

In deed, it has many same combinations.

Sean de Wolski on 25 May 2012

This is true. I messed up on thinking reshape() would account for the order of the cells being stacked. It did not, see update.

Answer by Daniel on 24 May 2012
```x = fullfact([3,3,3])-1
```