How to add random values into an empty vector repeatedly without knowing when it would stop? How to count average number of steps?

Imagine the process of forming a vector v by starting with the empty vector and then repeatedly putting a randomly chosen number from 1 to 20 on the end of v. How could you use Matlab to investigate on average how many steps it takes before v contains all numbers from 1 to 20? You can define/use as many functions or scripts as you want in your answer.

v=[];
v=zeros(1,20);

for a = 1:length(v)
  v(a)=randi(20);
end

since v is now only a 1x20 vector, if there are two numbers equal, it definitely does not have all 20 numbers from 1 to 20

for i = 1:length(v)
  for j = i+1:length(v)
    if v(i)==v(j) 
      v=[v randi(20)];
      i=i+1;
      break;
    end
  end
end



for k = 1:length(v)
  for n = 1:20
    if v(k)==n
      v=v;
    elseif v(k)~=n
      a=randi(20);
      v=[v a];
    end
    if a~=n
      v=[v randi(20)];
      k=k+1;
      break;
    end
  end
end

disp('number of steps: ')
i*k