[sicp] 1.11

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 process
#lang scheme

(define (f n)
  (cond ((= n 0) 0)
       ((= n 1) 1)
       ((= n 2) 2)
       (else (+ (f (- n 1))
               (* 2 (f (- n 2)))
               (* 3 (f (- n 3)))) ) ) )

- iterative process
#lang scheme

(define (f-iter a b c count)
   (if (= count 0)
     c
        (f-iter (+ a (* 2 b) (* 3 c) )
               a   b  (- count 1) ) ) )
    
(define (f n )
(f-iter 2 1 0 n) )