Nice recursive process and ugly iterative process

ex1.11.scm

@@ -0,0 +1,36 @@
+;; recursive process
+(define (f n)
+  (cond ((< n 3) n)
+        (else
+         (+
+          (f (- n 1))
+          (* 2 (f (- n 2)))
+          (* 3 (f (- n 3)))))))
+(define f-recur f)
+
+;; iterative process
+;; uses an accumulator `accu` to know when done
+(define (f n)
+  (define (f-iter n fn-1 fn-2 fn-3 accu)
+    (cond ((< n 3) n)
+          ((= accu n)
+           (+ fn-1 (* 2 fn-2) (* 3 fn-3)))
+          (else
+           (f-iter n
+                   (+ fn-1 (* 2 fn-2) (* 3 fn-3))
+                   fn-1
+                   fn-2
+                   (+ 1 accu)))))
+  (f-iter n 2 1 0 3))
+(define f-iter f)
+
+(define (check-f-up-to n)
+  (cond ((< n 3) (= (f-recur n) (f-iter n)))
+        (else
+         (and (= (f-recur n) (f-iter n))
+              (check-f-up-to (- n 1))))))
+
+(check-f-up-to 100)
+
+;Value: #t
+