how do I generate a binary matrix with specified number of 'ones' in each row & column?
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Is there any algorithm to do that?
回答(3 个)
Walter Roberson
2016-3-24
Because the number might be 1, this process is at least as difficult as the n- Rooks puzzle, the task of placing n chess rooks on a n x n board so that they cannot attack each other. You can find more information about the better studied n-Queens problem (diagonals have to be paid attention to) here
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Roger Stafford
2016-3-24
That would be impossible Nafila! Two ones in each column with six columns add up to a total of twelve ones, whereas four ones in each row with four rows add up to a total of sixteen ones. That can't be done.
Walter Roberson
2016-3-24
One thing you have not made clear is whether the task is to generate one such matrix at random, or if the task is to generate all such matrices given the parameters of size and number for row and column?
KSSV
2016-3-24
If you want a matrix where positions of 0, 1 are random. You may try round(rand(m,n)).
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Walter Roberson
2016-3-24
That will often not have the specified number of 1's in each row and column.
Image Analyst
2016-3-24
I think you might mean this:
% Specify 3 1's in each row.
numOnes = 3
% Create a 10 by 10 matrix of false/0's.
rows = 10;
columns = 15;
binaryMatrix = false(rows, columns);
% Go down row by row finding positions for numOnes 1's and assign them
for row = 1 : rows
% Get locations in this row.
oneLocations = randperm(columns, numOnes)
% Assign true/1 to those columns.
binaryMatrix(row, oneLocations) = true;
end
% Print final result to command window
binaryMatrix
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Image Analyst
2016-3-24
Oh wait, reading your comment to Walter it looks like you need the number in each column also to be a specified number. In that case, this code will not guarantee that since they're scrambled on a row-by-row basis and does not take other rows into account so you could have any number from 0 to rows in any given column, not necessarily the specified number you want.
Image Analyst
2016-3-24
By the way, for the special case of a square matrix where you want the same number in the rows and columns, you can do that. The concept is called "Latin Square" - you might want to research it.
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