From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Mon, 17 May 2010 10:37:10 +0000 (+0530)
Subject: Solution to 1.37. Iterative version needs some thinking.
X-Git-Url: https://git.rkrishnan.org/%5B/frontends/flags/%22file:/%22news.html/statistics?a=commitdiff_plain;h=16c1c210cb772d66faa3e5e5346a7bd3f921f0c1;p=sicp.git

Solution to 1.37. Iterative version needs some thinking.
---

diff --git a/src/sicp/ex1_37.clj b/src/sicp/ex1_37.clj
new file mode 100644
index 0000000..4e21e6a
--- /dev/null
+++ b/src/sicp/ex1_37.clj
@@ -0,0 +1,40 @@
+;; finite continued fraction
+;;
+;; f = N1/ (D1 + (N2/ D2 + (N3/ D3 + (.... + Nk/Dk))))
+
+(ns sicp.ex1_37
+  (:use [sicp utils]
+	[clojure.contrib test-is]))
+
+(defn- calc-cont-frac [n-fn d-fn k cnt]
+  (if (= cnt k)
+    (/ (n-fn cnt) (d-fn cnt))
+    (/ (n-fn cnt) (+ (d-fn cnt) (calc-cont-frac n-fn d-fn k (inc cnt))))))
+
+(defn cont-frac [n-fn d-fn k]
+  (calc-cont-frac n-fn d-fn k 1))
+
+(defn good-enough? [x y tolerance]
+  (< (abs (- x y)) tolerance))
+
+(deftest test-cont-frac-of-all-one
+  (is (good-enough? (/ 1.0 (cont-frac (fn [_] 1.0) (fn [_] 1.0) 100))
+		     1.618
+		     0.01)))
+
+;; iterative version
+;; work backwards from kth value to 1st value.
+(defn- calc-cont-frac-i [n-fn d-fn k cnt result]
+  (if (= cnt 0)
+    result
+    (calc-cont-frac-i n-fn d-fn k (dec cnt) (/ (n-fn cnt)
+					     (+ (d-fn cnt)
+						result)))))
+
+(defn cont-frac-iter [n-fn d-fn k]
+  (calc-cont-frac-i n-fn d-fn k k 0.0))
+
+(deftest test-cont-frac-iter-of-all-one
+  (is (good-enough? (/ 1.0 (cont-frac-iter (fn [_] 1.0) (fn [_] 1.0) 100))
+		    1.618
+		    0.01)))