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Problem 885. Create logical matrix with a specific row and column sums

Created by Amro

Given two numbers n and s, build an n-by-n 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:end-1)) sin(t(1:end-1))];
subplot(121), spy(M)
subplot(122), gplot(M, xy, '*-'), axis image

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Solution Statistics

28 correct solutions 14 incorrect solutions
Last solution submitted on Oct 16, 2014

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