how to build all binary vectors of length n whose number of its zero elements is m<n?

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Mahdi
Mahdi 2013-6-29
how to build all binary vectors of length n whose number of its zero elements is m<n?

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回答（2 个）

Image Analyst
Image Analyst 2013-6-29
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.
Roger Stafford
Roger Stafford 2013-6-29
编辑：Roger Stafford 2013-6-29
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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