SICP Exercise 1.37

continued-fractions.scm

;; Suppose that `n` and `d` are procedures of one argument (the term index `i`)
;; that return the N(i) and D(i) of the terms of the continued fraction. Define a
;; procedure cont-frac such that evaluating (cont-frac n d k) computes the value
;; of the k-term finite continued fraction:
;;
;;            N(1)
;; f = --------------------
;;               N(2)
;;     D(1) + ------------
;;           .      N(K)
;;            .  + ------
;;             .    D(K)

(define (cont-frac n d k)
  (if (= k 1)
      (/ (n k) (d k))
      (/ (n k) (+ (d k) (cont-frac n d (- k 1))))))

;; If your cont-frac procedure generates a recursive process, write one that
;; generates an iterative process.

(define (cont-frac n d k)
  (define (cf-iter a k)
    (if (= k 0)
        a
        (cf-iter (/ (n k) (+ (d k) a)) (- k 1))))
  (cf-iter 0 k))