# All possible combinations of 2 vectors.

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Artyom on 22 Nov 2012
Hi everyone.
I have one vector and one number. For example [1 3 5] and 0.
How do I generate all possible combinations? Like this:
0 3 5
1 0 5
1 3 0
0 0 5
0 3 0
1 0 0
0 0 0
##### 2 CommentsShowHide 1 older comment
Artyom on 22 Nov 2012
The rule is:
1) we have an n - dimensional vector.
2) replace one number with zero and find all combinations
3) replace two numbers with zero and find all combinations
4) ...
5) replace n-1 number with zero and find all combinations
6) replace n number with zero

Matt Fig on 22 Nov 2012
Edited: Matt Fig on 23 Nov 2012
Here is a solution:
function H = mycomb(V)
% Help
L = length(V);
H = cell(1,L);
for ii = 1:L-1
C = nchoosek(1:L,L-ii);
R = cumsum(ones(size(C)));
M = max(R(:,1));
H{ii} = zeros(M,L);
H{ii}(R+(C-1)*M) = V(C);
end
H{L} = zeros(1,L);
H = vertcat(H{:});
Now try it out from the command line:
>> mycomb([4 5 6])
ans =
4 5 0
4 0 6
0 5 6
4 0 0
0 5 0
0 0 6
0 0 0
>> mycomb([4 5 6 7])
ans =
4 5 6 0
4 5 0 7
4 0 6 7
0 5 6 7
4 5 0 0
4 0 6 0
4 0 0 7
0 5 6 0
0 5 0 7
0 0 6 7
4 0 0 0
0 5 0 0
0 0 6 0
0 0 0 7
0 0 0 0

### More Answers (3)

Andrei Bobrov on 22 Nov 2012
Edited: Andrei Bobrov on 22 Nov 2012
variant
t = [1 3 5];
ii = perms([t, zeros(size(t))]);
out = unique(sort(t(:,1:numel(t)),2),'rows');
or
t = [1 3 5];
out = [];
n = numel(t);
for jj = 1:n
k = nchoosek(t,n - jj);
out = [out;[zeros(size(k,1),jj),k]];
end
or
k = ones(1,numel(t)) * 2.^(numel(t)-1:-1:0)';
out = bsxfun(@times,t,dec2bin(0:k - 1,numel(t))-'0');
##### 1 CommentShowHide None
Matt Fig on 23 Nov 2012
Very nice! (The last one)

Azzi Abdelmalek on 22 Nov 2012
Edited: Azzi Abdelmalek on 23 Nov 2012
save this function
function y=arrangement(v,n)
m=length(v);
y=zeros(m^n,n);
for k = 1:n
y(:,k) = repmat(reshape(repmat(v,m^(n-k),1),m*m^(n-k),1),m^(k-1),1);
end
then type
x=arrangement([1 3 5 0],3)
out=x(~all(x,2),:)
If you don't need repetition add
s=arrayfun(@(t) sort(out(t,:)),(1:size(out,1))','un',0)
out1=unique(cell2mat(s),'rows')

Matt J on 23 Nov 2012
Edited: Matt J on 23 Nov 2012
t=[1 3 5];
n=length(t);
result = bsxfun(@times, [1,3,5], dec2bin(2^n-1:-1:0)-'0')