From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Sat, 10 Apr 2010 17:44:35 +0000 (+0530)
Subject: Added solution to 1.18. It is really really elegant problem and solution!
X-Git-Url: https://git.rkrishnan.org/specifications/banana.xhtml?a=commitdiff_plain;h=3853351fd0edd46ab600a1b6b68e2bd8a18a2a57;p=sicp.git

Added solution to 1.18. It is really really elegant problem and solution!
---

diff --git a/chapter1/ch1_2.clj b/chapter1/ch1_2.clj
index ed57832..0cf3c55 100644
--- a/chapter1/ch1_2.clj
+++ b/chapter1/ch1_2.clj
@@ -510,4 +510,29 @@ TRACE t2494: => -0.39980345741334
   (* 2 x))
 
 (defn half [x]
-  (/ x 2))
\ No newline at end of file
+  (/ x 2))
+
+;; exercise 1.18: iterative multiply thru addition
+;; the idea is to keep a state variable.
+(defn fast-mult-new [a b]
+  (fast-mult-iter a b 0))
+
+(defn fast-mult-iter [a b k]
+  (cond (= b 0) k
+	(even? b) (fast-mult-iter (twice a) (half b) k)
+	:else (fast-mult-iter a (- b 1) (+ k a))))
+
+(comment
+user> (dotrace [fast-mult-new fast-mult-iter] (fast-mult-new 2 3))
+TRACE t2915: (fast-mult-new 2 3)
+TRACE t2916: |    (fast-mult-iter 2 3 0)
+TRACE t2917: |    |    (fast-mult-iter 2 2 2)
+TRACE t2918: |    |    |    (fast-mult-iter 4 1 2)
+TRACE t2919: |    |    |    |    (fast-mult-iter 4 0 6)
+TRACE t2919: |    |    |    |    => 6
+TRACE t2918: |    |    |    => 6
+TRACE t2917: |    |    => 6
+TRACE t2916: |    => 6
+TRACE t2915: => 6
+6
+)