From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Thu, 27 May 2010 19:45:33 +0000 (+0530)
Subject: solution to 1.44. Extremely interesting problem
X-Git-Url: https://git.rkrishnan.org/pf/content/en/components/com_hotproperty/nxhtml.html?a=commitdiff_plain;h=7943585fa78030c9746c9c05706b5e02566f409d;p=sicp.git

solution to 1.44. Extremely interesting problem
---

diff --git a/src/sicp/ex1_44.clj b/src/sicp/ex1_44.clj
new file mode 100644
index 0000000..e6cf38b
--- /dev/null
+++ b/src/sicp/ex1_44.clj
@@ -0,0 +1,50 @@
+(ns sicp.ex1_44
+  (:use [clojure.contrib test-is]
+	[sicp utils]
+	[sicp ch1_3]
+	[sicp ex1_43]))
+
+(def dx1 0.00001)
+
+(defn smooth [f]
+  (fn [x]
+    (average (f (- x dx1))
+	     (f x)
+	     (f (+ x dx1)))))
+
+;; smooth takes a function as argument. repeated takes a function
+;; which needs to be repeated. Here it is the smooth function and
+;; the number of times it needs to be repeated. We call the function
+;; returned by repeated with f.
+(defn smooth-repeatedly [f n]
+  ((repeated smooth n) f))
+
+;; borrowing an idea from Drew Hess' solutions, we generate a test impulse
+;; function
+(defn impulse-maker [x a]
+  (fn [y] (if (= y x)
+	    a
+	    0)))
+
+;; we define a function which has an impulse at x=2 with a value 10.
+(defn my-impulse-func [x]
+  ((impulse-maker 2 10) x))
+
+(comment
+((smooth my-impulse-func) 2)
+;;=> 3.3333333
+user> ((smooth my-impulse-func) 1)
+;;=> 0.0
+user> ((smooth (smooth my-impulse-func)) 2)
+;;=> 3.3333333
+user> ((smooth (smooth (smooth my-impulse-func))) 2)
+;;=> 2.5925925
+
+;; now using our new function
+((smooth-repeatedly my-impulse-func 1) 2)
+;;=> 3.3333333
+user> ((smooth-repeatedly my-impulse-func 2) 2)
+;;=> 3.3333333
+user> ((smooth-repeatedly my-impulse-func 3) 2)
+;;=> 2.5925925
+)
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