How to find maximum square zero matrix through the biggest matrix?

Question

Serafettin Bal 2021-6-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/859140-how-to-find-maximum-square-zero-matrix-through-the-biggest-matrix

评论： Atsushi Ueno 2021-6-22

采纳的回答： Atsushi Ueno

how to plot a picture in matlab?

Below is the code that generates a random 6*6 diagonal square matrix.

And, the resulting random matrix (Mout) is here.

For example, the largest square zero matrix for this matrix is as follows.

4*4 Square zero matrix for the 6*6 square matrix.

So, how can I find the size of the maximum square zero matrix that can be created from this matrix?

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Rik 2021-6-22

编辑：Rik 2021-6-22

在 MATLAB Online 中打开

I recovered the removed content from the Google cache (something which anyone can do). Editing away your question is very rude. Someone spent time reading your question, understanding your issue, figuring out the solution, and writing an answer. Now you repay that kindness by ensuring that the next person with a similar question can't benefit from this answer.

There is also now a capture of the current state of this thread.

The image of the code was later replaced by this:

N = randi([6 6],1);
M = randi([0 1], N);
Mu = triu(M);
Ml = Mu';
Mout = Mu + Ml;
Mout = Mout - diag(diag(Mout));
G = graph(Mout,'lower');
plot(G)  

Atsushi Ueno 2021-6-22

@Rik Thank you for your recovering action. I can read back the comment left by the questioner in the history, so I will answer it.

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Answer 1

Atsushi Ueno 2021-6-18

2
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/859140-how-to-find-maximum-square-zero-matrix-through-the-biggest-matrix#answer_727850

在 MATLAB Online 中打开

What I did is:

Solving Find the biggest empty box - MATLAB Cody - MATLAB Central (mathworks.com)
Cheating other solution! --> "Finding 2D convolution with ones = 0" is the best idea
To find the square that can wrap across the edges: repmat(Mout,2) does work for the issue

If there are square zero matrices of the same size, the upper left one will be selected.

Sorry, it is not tested well.

N = randi([6 6],1);
M = randi([0 1], N);
Mu = triu(M);
Ml = Mu';
Mout = Mu + Ml;
Mout = Mout - diag(diag(Mout));
G = graph(Mout,'lower');
plot(G);
Mout4 = repmat(Mout,2);
for k = 1:length(Mout)
    [r,c] = find(~conv2(Mout4,ones(k),'valid'),1);
    if r
        k % k is the size of the square zero matrix
        r % r is the row index of the square zero matrix
        c % c is the column index of the square zero matrix
    end
end

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Atsushi Ueno 2021-6-19

I'm sorry. I got a lot of questions to answer, but I slept for 12 hours afterwards.

Atsushi Ueno 2021-6-22

>every runs (because Mout matris created randomly) return the same output. k=1 r=1 c=1 k=2 r=1 c=1

@Serafettin Bal Yes, most of the patters created randomly have small squares. Why don't you create some matrix has bigger chank of zero for testing? The logic I wrote finds the square of zero from smaller one to bigger one. And the last printed out 'k' is the size of the maximum square zero matrix.

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