dq03: Refactor factorial and make it tail recursive.

Use of result so far accumulator.

10-accumulators/dq03-factorial-tr.rkt

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+#lang htdp/isl
+
+;  PROBLEM 3:
+;
+;  Refactor the function below to make it tail recursive.
+;
+
+;; Natural -> Natural
+;; produces the factorial of the given number
+;(check-expect (fact 0) 1)
+;(check-expect (fact 3) 6)
+;(check-expect (fact 5) 120)
+#;
+(define (fact n)
+  (cond [(zero? n) 1]
+        [else
+         (* n (fact (sub1 n)))]))
+
+(define (fact n0)
+  ;; acc is Natural; the computation of the factorial so far.
+  ;; acc is a "result so far" type of accumulator.
+  ;; (fact 5 1) ; outer call
+  ;; (fact 5 1) ; 5
+  ;; (fact 4   5) ; 20
+  ;; (fact 3 20) ; 60
+  ;; (fact 2 60) ; 120
+  ;; (fact 1 120) ; 120
+  ;; (fact 0 120) ; 120
+  (local [(define (fact n acc)
+            ;; This takes one more recursion step.
+            ;(cond [(zero? n) acc]
+            (cond [(= n 1) acc]
+                  [else
+                   (fact (sub1 n) (* n acc))]))]
+    (fact n0 1)))
+