The maximum depth of the stack and the total number of pushes used in evaluating n!

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 :

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.

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