MATLAB: How to count the total number of recursion

collatzrecursion

Hello
I have a function
   function [out num] = collatz(val)
   num = 0;
   if val == 1
       out = 1;
   elseif mod(val, 2) == 0
       out = collatz(val/2);
   else 
       out= collatz(3*val+1);
   end
   k = num + 1;
   num = [num k]
   end
For the number of counts, num I keep getting num = [0 1] How do I count the total number of recursion that occurs? I heard that we can make a helper function but I have no idea how to make one. Thank you.

Best Answer

The problem is that you're not passing num to collatz, so how can it know how many times it has been called? Here is a version that makes num an optional argument, so you don't need to provide it in your call:
function [out, num] = collatz(val,varargin)
if nargin >1
    num = varargin{1};
else
    num = 0;
end
if val == 1
    out = 1;
elseif mod(val, 2) == 0
    [out,num] = collatz(val/2,num);
else
    [out,num] = collatz(3*val+1,num);
end
num = num+1;
Now if you try
[out,num] = collatz(4)
you get
out =
     1
num =
     3
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