how to create a list of random number with a minimum difference between each number?

Hi,

I am trying to create a list of 'n' random numbers within a range(1,m) and the difference between adjacent numbers need to be at least 'd'.

The list needs to be sorted and no repetion allowed.

I can do the same in python using

% r = m - ((m - 1) * (n - 1))
%   = 30 - ((3-1) * (6-1)) = 30 - 2*5 = 20
%[(d-1)*i + x for i, x in enumerate(sorted(random.sample(range(r), n)))]
print([2*i + x for i, x in enumerate(sorted(random.sample(range(20), 6)))])
>>[2, 5, 14, 20, 24, 28]

In the above code, I am trying to generate a sorted list of 6 random numbers from 0-30, with a minimum difference between each adjacent element of at least 3.

Can some one plese suggest me how can I do something similar in matlab?

[Torsten]

Not clear. Could you give an example ?

If the range is 1:100 and d = 6, you expect something like

v = 98 91 80 74 60 ...

such that v(1:n-1) -v(2:n) >= 6

?

[Raghav Rathi]

Yes, that's how it would be.

[Torsten]

So the above output

[2, 5, 14, 20, 24, 28]

is wrong ?

[Raghav Rathi]

That is correct output, in that output, d=3, n=6 and m = 30. But I got that output using python. I am trying to write a similar code in MATLAB but I am unable to do so. I am not that experienced with MATLAB.

[Raghav Rathi]

So, above what I did is, I was trying to generate 6 random numbers from 0-30, with a minimum difference between each adjacent element of at least 3.

[Torsten]

But the numbers are in the wrong order, at least according to your description.

[Raghav Rathi]

I am sorry for the confussion, I have corrected my explaination.

[Torsten]

So the list of numbers does not need to be increasing or decreasing ?

[Raghav Rathi]

It can be either.

[Torsten]

So [2 14 4 28 20 4] (not ordered, repetitions allowed) (d=3, n=6 and m = 30) would be acceptable in your test case ?

[Raghav Rathi]

Sorry for the confussion again, by either I meant, it can either be increasing or decresing.

If you take [2 14 4 28 20 4], after sorting it will be [2 4 4 14 20 28 ], and the difference between 1st 3 elements is less than 3 so it wont be acceptable. if it was [2 5 8 14 20 28 ] then it would be acceptable.

Answer 1

[David Hill]

You can brute force it.

m=200;%randomn numbers between 1-200
n=50;%array length
d=20;%minimum distance
a=randi(m,100000,n);%make sifficiently large
D=abs(diff(a,[],2));
idx=D>=d;
f=find(sum(idx,2)==n-1);
randNums=a(f,:);%rows of array having randomn numbers with adjacent elements being at least d apart

[Torsten]

How do you want to get a sorted array of length 50 with elements minimum 10 apart if you only choose random numbers between 1-200 ? Maximum array length in this case is 20 .

[David Hill]

Missed part of the question.

[David Hill]

Below works but the randomn numbers will be skewed towards the high-side of the interval.

m=2000;
n=10;
d=5;
r=1:m;
R=[];
while 1
 for k=1:n
   if length(r)+k<n||isempty(r)
       r=1:m;
       R=[];
       break;
   end
   p=randperm(length(r),1);
   R=[R,r(p)];
   r=r(r>(r(p)+d));
 end
 if ~isempty(R)
     break;
 end
end

[Raghav Rathi]

Thank you David.