SICP Goodness - Continued Fraction

SICP Exercise 1.37

1 minute read

Do you think Computer Science equals building websites and mobile apps?

Are you feeling that you are doing repetitive and not so intelligent work?

Are you feeling a bit sick about reading manuals and copy-pasting code and keep poking around until it works all day long?

Do you want to understand the soul of Computer Science?

If yes, read SICP!!!

Writing recursive functions is not an easy task, often requires a different way of thinking.

For practice purpose, let’s now take a look at an exercise from the book.

Recursive Process

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

(define (cont-frac n d k)
  (cont-frac-iter n d k 1))

Iterative Process

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

(define (cont-frac n d k)
  (cont-frac-iter n d k (/ (n k) (d k))))

Tips

The two types of recursive procedure can be illustrated below.

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