Exercise 1.11 from SICP

exercise.scm

(define (f-11-tree n)
  (define (f n depth)
    (println-depth depth n)
    (if (< n 3)
        n
        (+ (f (- n 1) (inc depth))
           (* 2 (f (- n 2) (inc depth)))
           (* 3 (f (- n 3) (inc depth))))))
  (f n 0))

;; a <- a + 2b + 3c
;; b <- a
;; c <- b

(define (f11-iter a b c n)
  (println a b c n)
  ;; degenerate cases
  (cond ((= 2 n) a)
        ((= 1 n) b)
        ((= 0 n) c)
        (else
         (f11-iter (+ a (* 2 b) (* 3 c))
                   a
                   b
                   (dec n)))))

(define (f11 n)
  (f11-iter 2 1 0 n))