how to build all binary vectors of length n whose number of its zero elements is m<n?
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how to build all binary vectors of length n whose number of its zero elements is m<n?
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Image Analyst
on 29 Jun 2013
If you specify m, and want all binary vectors with length longer than m, then there is an infinite number of vectors satisfying that. For example
m = 4;
output = false(1, 7) % This one has length 7.
output = false(1, 42) % This one has length 42.
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Roger Stafford
on 29 Jun 2013
Edited: Roger Stafford
on 29 Jun 2013
N = 0;
for k = 0:m
N = N + nchoosek(n,k);
end
A = ones(N,n);
q = 1;
for k = 1:m
p = nchoosek(1:n,k);
for r = 1:size(p,1)
q = q+1;
A(q,p(r,:)) = 0;
end
end
The n-element rows of array A have all possible combinations of ones and zeros in which there are no more than m zeros. I assumed here that m and n were fixed quantities which you specify.
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