Problem 885. Create logical matrix with a specific row and column sums
Given two numbers n and s, build an nbyn logical matrix (of only zeros and ones), such that both the row sums and the column sums are all equal to s. Additionally, the main diagonal must be all zeros.
You can assume that: 0 < s < n
Example:
Take n=10 and s=3, here is a possible solution
M = 0 1 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0
Note that the following conditions are all true:
all(sum(M,1)==3) % column sums equal to s all(sum(M,2)==3) % row sums equal to s all(diag(M)==0) % zeros on the diagonal islogical(M) % logical matrix ndims(M)==2 % 2D matrix all(size(M)==n) % square matrix
Unscored bonus:
Visualize the result as a graph where M represents the adjacency matrix:
% circular layout t = linspace(0, 2*pi, n+1)'; xy = [cos(t(1:end1)) sin(t(1:end1))]; subplot(121), spy(M) subplot(122), gplot(M, xy, '*'), axis image
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Problem Comments

2 Comments
Any clue? Does this problem require great mathematics abilities ?
Not really, imagine in the simplest case that we could use the diagonals (ignoring this constraint), what the solution would look like? A chessboard pattern would solve it, wouldn't it? Now, how can we work around the constraint?
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