random order of elements in array meeting some conditions

Hello!

I have a vector with levels:

levels = [20:5:80];

I am randomizing the order of presentation so that every level is used during my experiment:

b = levels(randperm(numel(levels)));

However, I want to make sure that there will be no situation that the subsequent numbers will not be higher than the previous one than 30, e.g.

b = 60 55 80 35 65 25 30 40 75 50 20 45 70;

I wrote this loop (see below) however it does not ensure my condition, it just randomise the order again... How can I modify it to make sure that?

for l = 2:(length(b)-1)
    if b(l)-b(l-1)>=30
        b = levels(randperm(numel(levels)));
    end
end

[Adam]

How 'random' do you need them to be? Obviously you could randomise them within blocks of 30 to ensure the condition, but that isn't especially random overall.

Answer 1

[Bruno Luong]

Dynamic programming

rpermc()

%% save the rest in rpermc.m if needed
function r = rpermc()
while true
    r = rpc([], 20:5:80, 30);
    if ~isempty(r)
        return
    end
end

end

% subfunction
function r = rpc(r, s, dmax)
if isempty(s)
    return
else
    if isempty(r)
        b = true(size(s));
    else
        b = s < r(end)+dmax;
    end
    if any(b)
        i = find(b);
        i = ceil(rand*length(i));
        r = [r s(i)];
        s(i) = [];
        r = rpc(r, s, dmax);
    else
        r = [];
    end
end
end

[Katarzyna Dragun]

this is wonderful! thanks a lot:):)

Answer 2

[Rik]

I'm not aware of any method that can do what you want. In the mean time, you can use the code below to improve the efficiency of your brute force method. Note that this does not check if there actually exists a valid permutation.

levels = 20:5:80;

satisfies_condition=@(x) all(diff(x)<30);
b = levels(randperm(numel(levels)));
while ~satisfies_condition(b)
    b = levels(randperm(numel(levels)));
end