随笔分类(157)

Exercise 1.11.  A function f is defined by the rule that f(n) = n if n<3 and f(n) = f(n - 1) + 2f(n - 2) + 3f(n - 3) if n> 3. Write a procedure that computes f by means of a recursive process. Write a procedure that computes f by means of an iterative process.

recursive:

(define (fn n)
  (cond ((>= n 3) (+ (+ (fn (- n 1)) (* 2 (fn (- n 2)))) (* 3 (fn (- n 3)))))
        ((< n 3) n)
   ))

 iterative:

(define (re n)
  (if (< n 3)
      n
      (iter 2 1 0 n)
      ))
(define (iter a b c n)
(if(= n 3)
   (ca a b c)
   (iter (ca a b c) a b (- n 1))
   )
)
(define (ca a b c)
  (+ a (* 2 b) (* 3 c) )
)