How to calculate how many recursive calls happened in this Haskell function?

Question

I\'ve been trying to figure this out for a couple of hours now. I need to calculate how many recursive calls happened using a certain function:

maximum\' ::         


        

Answer 1

For a list with n elements, there are n-1 recursive calls. To make it easier to see, we'll rewrite the function slightly. (We can ignore empty list for this.)

maximum' [x] = x
maximum' (x:xs) = if x > maxTail then x else maxTail
                  where maxTail = maximum' xs

A recursive call is made when the tail of the argument is not empty. (Note that a function that was defined for the empty list as well would make n recursive calls on a list with n items.)

We can expand a call to a 3-item list, for example:

maximum' [1,2,3] = if 1 > maxTail then 1 else maxTail where maxTail = maximum' [2,3]
 maximum' [2,3] = if 2 > maxTail then 2 else maxTail where maxTail = maximum' [3]
  maximum' [3] = 3