.

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

``````(define (recursive-f n)
(if (< n 3)
n
(+ (recursive-f (- n 1))
(* 2 (recursive-f (- n 2)))
(* 3 (recursive-f (- n 3))))))
``````

### Iterative process

`counter` counts up from 3 to `n`. `a` represents f(`counter` - 3), `b` represents f(`counter` - 2), and `c` represents f(`counter` - 1).

``````(define (iterative-f n)
(define (iter-f a b c counter)
(if (= counter n)
(+ (* 3 a) (* 2 b) c)
(iter-f b c (+ (* 3 a) (* 2 b) c) (+ counter 1))))
(if (< n 3)
n
(iter-f 0 1 2 3)))
``````

Note 1: It seems more natural to me to count up to `n` rather than back from `n`, since the process calculates from lower numbers to higher numbers.

Note 2: Since the definition of `iter-f` is inside the definition of `interative-f`, we can use `n` inside the definition of `iter-f` without having to pass it in as an argument.