MATLAB: Tricky randomization issue – help needed!

pairingrandomizationrandomizeshuffling

Dear Matlab folks,
I am struggling with the following issue:
I created 80 parings of numbers. These pairings should stay the same but the order of the pairings should be randomized.
So, I have a variable containing these pairings: sequence = [pairing_1 pairing_2 pairing_3 and so forth].
How can I randomize the order of these pairings? For example, it would look like this then: randomized_sequence = [pairing_2 pairing_3 pairing_1 …..]
And now for the tricky part:
The numbers of the pairings reach from 1 to 40. Every number from 1 to 40 is combined with one random even number between 1 and 40 and one random uneven number between 1 and 40. For 1, I could have the pairings 1 & 18 and 1 & 9 for example. But 1 must not be paired with 1! No number can be matched with itself. Furthermore, 1 must not be paired with 2 and 2 must not be paired with 1, the sequence doesn't matter. 3 must not be paired with 4, 5 must not be paired with 6 and so forth until 39 must not be paired with 40 and every time, the sequence doesn't matter. So, 39 and 40 is not possible as well as 40 and 39.
The numbers that must not be paired are:
1 2 | 3 4 | 5 6 | 7 8 | 9 10 | 11 12 | 13 14 | 15 16 | 17 18 | 19 20 | 21 22 | 23 24 | 25 26 | 27 28 | 29 30 | 31 32 | 33 34 | 35 36 | 37 38 | 39 40
So 2 and 3 can be paired, for example!
Now the problem is, if I have these 2 pairings 14 16 and 16 9 and after the shuffling of the pairings 14 16 lands before 16 9 then I have a 16 16 pairing as well which must not happen. Such unwanted pairings can happen a lot through the shuffling. For example, the 14 of 14 16 must not be preceeded by 14 or 13 and the 16 of 14 16 must not be followed by 16 or 15.
I was thinking about maybe coding something like: "If 1 is followed/preceded by 1 or 2 then shuffle again. If 2 is followed/preceded by 1 or 2 then shuffle again. If 3 is followed/preceded by 3 or 4 then shuffle again…." and so forth until "If 40 is followed/preceded by 40 or 39 then shuffle again."
What do you think, is there a way to do it like that? Or even a way easier solution, I did not think about?
I very much appreciate any help, this is bothering me since quite some time now.
Thanks in advance,
Rupert

Best Answer

Because we now have a proper definition of the problem we can start writing the code for the solution:
rng(1)%set a random seed so the results are repeatable
N=6;%define the problem size here
all_ids=(1:N)';
odd=1:2:N;even=2:2:N;
% %these are the steps in the while condition:
% step1=sequence+mod(sequence,2);%'round' to an even number: [1 2 3] --> [2 2 4]
% step2=diff(step1);%find delta between each successive number
% step3=step2==0;%if the delta was zero, that means either [1 2] (or [2 1]) or [2 2]
% sequence_is_invalid=any(step3);%any invalid pair makes the whole sequence invalid
n=0;
sequence=[1 1];%enter loop by using an invalid sequence
while any(diff(sequence+mod(sequence,2))==0)
    n=n+1;
    pair_with_even=even(randi(end,N,1)).';
    pair_with_odd=odd(randi(end,N,1)).';
    list_of_pairs=[all_ids pair_with_odd;all_ids pair_with_even];
    list_of_pairs([1:2:end 2:2:end],:)=list_of_pairs;
    sequence=reshape(list_of_pairs.',1,[]);
end
clc,fprintf('generating the sequence below took %d tries\n',n),fprintf('%d ',sequence);fprintf('\n')
You can also shuffle the order of list_of_pairs:
shuffled=list_of_pairs(randperm(end),:);
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