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.
递归过程非常容易写出来。只需要根据函数定义就可以。
(define (f/rec n)
(cond ((< n 3) n)
(else
(+ (f/rec (- n 1))
(* 2 (f/rec (- n 2)))
(* 3 (f/rec (- n 3)))))))
对于迭代的版本，我们必须知道，迭代的过程在每次迭代中都保存了当前的结果，它不可能像递归那样去为了得到 fn 的值才去计算 fn-1 的值，所以迭代总是从 n 可以取的某一个边界值开始，一直迭代到 n 的另外一个边界值。
(define (f/iter n)
(define (iter fn-1 fn-2 fn-3 counter)
(cond ((< n 3) n)
((> counter n) fn-1)
(else
(iter (+ fn-1 (* 2 fn-2) (* 3 fn-3))
fn-1 fn-2
(+ counter 1)))))
(iter 2 1 0 3))
;;; tests begin
(load "../testframe.scm")
(for-each (lambda (x)
(assert= (f/rec x) (f/iter x)))
'(1 2 3 4 5 6 7 8 9 10))