Exercise 5.27.  For comparison with exercise 5.26, explore the behavior 
of the following procedure for computing factorials recursively:

(define (factorial n)
  (if (= n 1)
      1
      (* (factorial (- n 1)) n)))

By running this procedure with the monitored stack, determine, as a 
function of n, the maximum depth of the stack and the total number of 
pushes used in evaluating n! for n > 1. (Again, these functions will be 
linear.) Summarize your experiments by filling in the following table 
with the appropriate expressions in terms of n:

  Maximum depth   Number of pushes
Recursive     
factorial     
Iterative     
factorial     

The maximum depth is a measure of the amount of space used by the 
evaluator in carrying out the computation, and the number of pushes 
correlates well with the time required. 

————————————————————————————————————————————————————————————————————————

;;; EC-Eval input:
(factorial 3)
(total-pushes = 80 maximum-depth = 18)

(factorial 4)
(total-pushes = 112 maximum-depth = 23)

              depth         pushes

recursive     5n + 3        32n - 16

iterative     10            35n + 29

For n=5, we expect depth=28, pushes=144, testing:

;;; EC-Eval input:
(factorial 5)
(total-pushes = 144 maximum-depth = 28)