Create matrix (30 x 12) with numbers from 1 to 12 without repetition without any repetitions of following numbers for each row

Hi all,

I want to create a matrix (30 rows, 12 columns) with numbers from 1 to 12. Each row should be as unique as possible, so that two numbers are barely following each other.

For example:

11 3 8 9 12 4 10 5 1 7 6 2

6 7 5 1 4 9 12 3 8 2 11 10

In this case of only 2 rows 8 follows 3 and 12 follows 9. This is what I want to avoid.

Can anyone help me out?

Thanks in advance!

[JA]

I'm aware of that issue. My goal is to have as least repetitions as possible.

Answer 1

[JESUS DAVID ARIZA ROYETH]

here the solution:

A=randperm(12);
iterac=500;
for k=1:30-1
    it=0;
while true
it=it+1;
b=randperm(12);
c2=[diff(b); b(1:end-1) .* b(2:end)];
cd=0;
for j=1:size(A,1)
c=[diff(A(j,:)); A(j,1:end-1) .* A(j,2:end)];
if size(intersect(c',c2','rows'),1)<=1 || (size(intersect(c',c2','rows'),1)<=2 && it>iterac)
    cd=cd+1;
end
end
if cd==size(A,1)
    A(end+1,:)=b;
    break
end
end
end
disp(A)

Answer 2

[Bhaskar R]

Uniformly distributed pseudorandom integers using the command

randi

may produce as you require

mat = randi([1, 12], 30, 12)

[JA]

Using this, there are repetitions of numbers within a row, e.g.

9 5 5 3 12 11 2 10 1 4 9 10

Is there any possibility to avoid this on top of the other requirements?

[Bhaskar R]

You can refere this answer

https://in.mathworks.com/matlabcentral/answers/356256-generating-unique-random-numbers-less-than-1-in-matrix#answer_281525

Answer 3

[Matt J]

Note that there are only

>> nchoosek(12,2)*2
ans =
   132

distinct subsequences of length 2 that can be drawn from the numbers 1-12, and a 30x12 matrix contains 330 such sequences. So, it is inevitable that the result will contain several hundred repetitions.

However, you might wish to consider the following as a way to diminish the similarities between rows.

m=12;
n=30;
k=n*100;

[~,P]=sort(rand(k,12),2);

D=pdist2(P,P);


[~,I]=maxk(max(D,[],2),n);

I=nan(1,n);
I(1)=1;
for k=1:n-1
   
    i=I(k);
    [~,j]=max(D(i,:),[],2);
    D(i,:)=nan; D(:,i)=nan;
    I(k+1)=j;
    
end

result=P(I,:)