ex1_11.scm

;Exercise 1.11 - Given a function f, define two versions of 
; a procedure that computes f, one which generates a 
; tree recursive process, and one that generates an 
; iterative process.

;recursive version:
(define (f n)
  (if (< n 3)
      n
      (+ (f (- n 1)) 
	 (* 2 (f (- n 2))) 
	 (* 3 (f (- n 3))))))


;iterative version:
(define (f n)
  (define (f-comp a b c)
    (+ a 
       (* 2 b)
       (* 3 c)))
  (define (f-iter count nm1 nm2 nm3)
    (if (= 0 count)
	(f-comp nm1 nm2 nm3)
	(f-iter (dec count) (f-comp nm1 nm2 nm3) nm1 nm2)))
  (if (< n 3)
      n
      (f-iter (- n 3) 2 1 0)))