permute with exact repeats

Question

mark palmer 2023-12-12

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https://ww2.mathworks.cn/matlabcentral/answers/2059889-permute-with-exact-repeats

评论： Dyuman Joshi 2023-12-13

I'm trying to permute a comprehensive list of 3 elements, say [1 2 3]

over a 5-size array with at least 1 element included from the 3 element array. (I'd like it the result be general, so the variables might be 3 over 6, 4 over 7, etc.) Obviously I can do this by brute force but I'd prefer a more elegant solution.

The result would be

1 1 1 2 3

1 1 1 3 2

1 1 2 1 3

1 1 2 3 1

1 1 3 1 2

1 1 3 2 1

1 1 3 2 2

1 1 3 3 2

1 2 1 1 3

1 2 1 2 3

...

3 3 3 2 1

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Answer 1

Voss 2023-12-12

1
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https://ww2.mathworks.cn/matlabcentral/answers/2059889-permute-with-exact-repeats#answer_1370394

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Here's one way:

x = [1 2 3];
n = 5;
% generate a matrix M whose rows are all possible
% sets of n elements from x:
m = numel(x);
M = x(1+dec2base(0:m^n-1,m)-'0');
% remove rows of M that don't have each element 
% of x at least once:
for ii = 1:m
    M(~any(M == x(ii),2),:) = [];
end
disp(M)
   1     1     2     3
   1     1     3     2
   1     2     1     3
   1     2     2     3
   1     2     3     1
   1     2     3     2
   1     2     3     3
   1     3     1     2
   1     3     2     1
   1     3     2     2
   1     3     2     3
   1     3     3     2
   2     1     1     3
   2     1     2     3
   2     1     3     1
   2     1     3     2
   2     1     3     3
   2     2     1     3
   2     2     2     3
   2     2     3     1
   2     2     3     2
   2     2     3     3
   2     3     1     1
   2     3     1     2
   2     3     1     3
   2     3     2     1
   2     3     2     2
   2     3     2     3
   2     3     3     1
   2     3     3     2
   2     3     3     3
   3     1     1     2
   3     1     2     1
   3     1     2     2
   3     1     2     3
   3     1     3     2
   3     2     1     1
   3     2     1     2
   3     2     1     3
   3     2     2     1
   3     2     2     2
   3     2     2     3
   3     2     3     1
   3     2     3     2
   3     2     3     3
   3     3     1     2
   3     3     2     1
   3     3     2     2
   3     3     2     3
   3     3     3     2
   1     1     1     3
   1     1     2     3
   1     1     3     1
   1     1     3     2
   1     1     3     3
   1     2     1     3
   1     2     2     3
   1     2     3     1
   1     2     3     2
   1     2     3     3
   1     3     1     1
   1     3     1     2
   1     3     1     3
   1     3     2     1
   1     3     2     2
   1     3     2     3
   1     3     3     1
   1     3     3     2
   1     3     3     3
   2     1     1     3
   2     1     2     3
   2     1     3     1
   2     1     3     2
   2     1     3     3
   2     2     1     3
   2     2     3     1
   2     3     1     1
   2     3     1     2
   2     3     1     3
   2     3     2     1
   2     3     3     1
   3     1     1     1
   3     1     1     2
   3     1     1     3
   3     1     2     1
   3     1     2     2
   3     1     2     3
   3     1     3     1
   3     1     3     2
   3     1     3     3
   3     2     1     1
   3     2     1     2
   3     2     1     3
   3     2     2     1
   3     2     3     1
   3     3     1     1
   3     3     1     2
   3     3     1     3
   3     3     2     1
   3     3     3     1
   1     1     1     2
   1     1     2     1
   1     1     2     2
   1     1     2     3
   1     1     3     2
   1     2     1     1
   1     2     1     2
   1     2     1     3
   1     2     2     1
   1     2     2     2
   1     2     2     3
   1     2     3     1
   1     2     3     2
   1     2     3     3
   1     3     1     2
   1     3     2     1
   1     3     2     2
   1     3     2     3
   1     3     3     2
   2     1     1     1
   2     1     1     2
   2     1     1     3
   2     1     2     1
   2     1     2     2
   2     1     2     3
   2     1     3     1
   2     1     3     2
   2     1     3     3
   2     2     1     1
   2     2     1     2
   2     2     1     3
   2     2     2     1
   2     2     3     1
   2     3     1     1
   2     3     1     2
   2     3     1     3
   2     3     2     1
   2     3     3     1
   3     1     1     2
   3     1     2     1
   3     1     2     2
   3     1     2     3
   3     1     3     2
   3     2     1     1
   3     2     1     2
   3     2     1     3
   3     2     2     1
   3     2     3     1
   3     3     1     2
   3     3     2     1

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mark palmer 2023-12-13

Thanks both that was quick and very helpful!

Voss 2023-12-13

You're welcome!

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Answer 2

Cris LaPierre 2023-12-12

2
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https://ww2.mathworks.cn/matlabcentral/answers/2059889-permute-with-exact-repeats#answer_1370414

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I think this does what you are looking for.

v = 1:3;
% create all 5-digit possible combinations
T = table2array(combinations(v,v,v,v,v));
% Extract only those that contain a 3 numbers
idx = any(T==1,2) & any(T==2,2) & any(T==3,2);
T = T(idx,:)
T = 150×5
     1     1     1     2     3
     1     1     1     3     2
     1     1     2     1     3
     1     1     2     2     3
     1     1     2     3     1
     1     1     2     3     2
     1     1     2     3     3
     1     1     3     1     2
     1     1     3     2     1
     1     1     3     2     2

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Adam Danz 2023-12-13

编辑：Adam Danz 2023-12-13

在 MATLAB Online 中打开

Great idea to use combinations (R2023a and later).

I fiddled with your solution a bit to make it flexibly receive any number of combinations.

v = 1:3;
n = 5; 
% create all 5-digit possible combinations
in = repelem({v},1,n); 
A = table2array(combinations(in{:}));
% Extract only those that contain a 3 numbers
c = arrayfun(@(x)any(ismember(A,x),2),v,'UniformOutput',false);
rm = ~all([c{:}],2);
A(rm,:) = []
A = 150×5
     1     1     1     2     3
     1     1     1     3     2
     1     1     2     1     3
     1     1     2     2     3
     1     1     2     3     1
     1     1     2     3     2
     1     1     2     3     3
     1     1     3     1     2
     1     1     3     2     1
     1     1     3     2     2