MATLAB: Calculate a randomized array with some constraints.

arrayconstraintslagMATLABpsychologyrandomizationstep size

Hello, for a psychological experiment I have the following problem. I need to calculate an array containing 70 distinct numbers. From these 70 numbers are 20 pairs (so e.g. two 1s, two 2s, two 3s etc.), all other numbers are zeros. The constraint is now that all pairs shall have a fixed index step-size to each other (e.g. if the step-size=2 and the first 3 lays at index 2, than the second 3 must lay at index 4), but apart from that the array should be completely random. The step-size should be variable between n=2 to n=20. Whether two pairs overlap (e.g. that if the step-size=2, and the first pair lays at index 2 and 4, and the second pair lays at index 3 and 5), doesn’t matter. Also how long Matlab needs, to find such an Array does not really matter, as long it does not take more than an hour or so.
Does anyone have an idea how I can tell Matlab to output me such an array? This is what I tried so far:
    myArray = [zeros(1,40),1:20,1:20]; % the array that shall be randomized,
                                       % under the bespoken constraint. 
    lags = 2;   % variable step-size
    pairs = 20; % number of pairs
    a=0;
    while a==0
        myArray = myArray(randperm(length(myArray))); % new randomization, new chance!
        for i=1:pairs
           tmp = find(myArray==i);
           if tmp(1)+lags~=tmp(2);     % if one pair has not the right index 
                                       %stepsize, interrupt for-loop.
               break;
           elseif i==pairs
               a=1;            % if all numbers are at their right 
                               % place stop the while loop
        end    
    end
However, I have to admit that this is totally bruteforce and in fact does never end (at least not within one hour ;-)).
I would be very very glad if someone could help me out with a smarter approach. Cheers.

Best Answer

pairs = [1 1; 2 2; 3 3; 4 4];
your_array = zeros(1,20);
step_size = 4;
numPairs = size(pairs,1);
pos = 1:numel(your_array);
for ii = 1:numPairs
    %pick a pair
    idx = randi(size(pairs,1));
    current_val = pairs(idx,1);
    %Pick starting position
    posIdx = randperm(numel(pos)-step_size,1);
    your_array([pos(posIdx) pos(posIdx)+step_size]) = current_val;
    %Make it so the same positions cannot be picked again
    pos([posIdx posIdx+step_size]) = [];
    pairs(idx,:) = [];
end
disp(your_array)
Please accept an answer once it has solved your problem.
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