Showing every possibility of each index in a matrix

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Hardi Mohammed 2020-1-26

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回答： Image Analyst 2020-1-26

I am trying to find out all the possibility of Matrix index. but I have problem for example:

A=[ 1 2 3; 
    4 5 6; 
    7 8 9];

Here we have six possibilities

1 5 9

1 6 8

2 4 9

2 6 7

3 5 7

3 4 8

The above rows are the possibilities of A matrix. I am trying to get a matrix with all these possiblities but I have problem. Does someone know how we can do it in MATLAB?

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Mohammad Sami 2020-1-26

编辑：Mohammad Sami 2020-1-26

Would the number of possibilities be n factorial for n x n matrix ?

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Answer 1

Image Analyst 2020-1-26

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https://ww2.mathworks.cn/matlabcentral/answers/502020-showing-every-possibility-of-each-index-in-a-matrix#answer_412083

在 MATLAB Online 中打开

Sounds like homework so I'll just give a hint. If it's not homework, say so.

The list seems to start only with elements on the first row and include elments on the second and third row only if the column is not the same as the column that the element in the top row is. Put in a counter and an if with a continue if the column is the same. Here's a start

topRow = A(1, :);
[rows, columns] = size(A)
counter = 1
results = zeros(1, columns); % Initialize
for col = 1 : columns
    for row2Col = 1 : columns
        if ........
                continue
        end
        for row3Col = 1 : columns
            if ............
                continue; % Skip
            end
            % String together all elements that we've found that meet criteria.
            results(counter, :) = [A(1, col), A(2, row2Col), A(3, row3Col)]
            counter = counter + 1;
        end
    end
end
results % Report to command window.