From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Tue, 18 May 2010 13:31:41 +0000 (+0530)
Subject: A much better way to generate the denominator sequence.
X-Git-Url: https://git.rkrishnan.org/FOOURL?a=commitdiff_plain;h=f0ef016256924a3e47e075495560138f1f5a9721;p=sicp.git

A much better way to generate the denominator sequence.
---

diff --git a/src/sicp/ex1_38.clj b/src/sicp/ex1_38.clj
index 54acde7..07bb2e5 100644
--- a/src/sicp/ex1_38.clj
+++ b/src/sicp/ex1_38.clj
@@ -9,14 +9,17 @@
     (concat [0 1] (interleave s1 s2 s2))))
 ;; we concat [0 1] because nth sequences are indexed from 0 
 
+(defn den-seq [k]
+  (if (= (rem k 3) 2)
+    (* (/ (+ k 1) 3) 2) ;; ((k+1)/3)*2
+    1))
+
 ;; approximating e
 (defn e-approximation [len]
-  (let [l (* 3 (int (/ len 3.0)))
-	den (gen-sequence l)]
-    (+ 2.0
-       (cont-frac (fn [k] 1.0)
-		  (fn [k] (nth den k))
-		  l))))
+  (+ 2.0
+     (cont-frac (fn [k] 1.0)
+		(fn [k] (den-seq k))
+		len)))
 
 (comment
 user> (e-approximation 10)
@@ -31,4 +34,5 @@ user> (e-approximation 60)
 2.7182818284590455
 user> (e-approximation 100)
 2.7182818284590455
-)
\ No newline at end of file
+)
+