From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Mon, 17 May 2010 08:01:45 +0000 (+0530)
Subject: Solution to 1.36.
X-Git-Url: https://git.rkrishnan.org/vdrive/%22news.html/simplejson//%22%22.?a=commitdiff_plain;h=b1d84232d29f1b6fc3ac980188d55bc4e66ee1b9;p=sicp.git

Solution to 1.36.
---

diff --git a/src/sicp/ex1_36.clj b/src/sicp/ex1_36.clj
new file mode 100644
index 0000000..5de257a
--- /dev/null
+++ b/src/sicp/ex1_36.clj
@@ -0,0 +1,89 @@
+;; Exercise 1.36.  Modify fixed-point so that it prints the sequence
+;; of approximations it generates, using the newline and display
+;; primitives shown in exercise 1.22. Then find a solution to
+;; x^x = 1000
+;; by finding a fixed point of x |->  log(1000)/log(x).
+;;
+;; Compare the number of steps this takes with and without average damping.
+(ns sicp.ex1_36
+  (:use [sicp utils]
+	[clojure.contrib test-is]))
+
+(defn close-enough? [x y tolerance]
+  (< (abs (- x y)) tolerance))
+
+(defn fixed-point [f guess]
+  (let [next (f guess)
+	nsteps 0]
+    (do
+      (println "new guess is " next)
+      (if (close-enough? next guess 0.00001)
+	next
+	(fixed-point f next)))))
+
+;; fixed point
+(comment
+(fixed-point #(/ (Math/log 1000) (Math/log %)) 1.1)
+new guess is  72.47657378429035
+new guess is  1.6127318474109593
+new guess is  14.45350138636525
+new guess is  2.5862669415385087
+new guess is  7.269672273367045
+new guess is  3.4822383620848467
+new guess is  5.536500810236703
+new guess is  4.036406406288111
+new guess is  4.95053682041456
+new guess is  4.318707390180805
+new guess is  4.721778787145103
+new guess is  4.450341068884912
+new guess is  4.626821434106115
+new guess is  4.509360945293209
+new guess is  4.586349500915509
+new guess is  4.535372639594589
+new guess is  4.568901484845316
+new guess is  4.546751100777536
+new guess is  4.561341971741742
+new guess is  4.551712230641226
+new guess is  4.558059671677587
+new guess is  4.55387226495538
+new guess is  4.556633177654167
+new guess is  4.554812144696459
+new guess is  4.556012967736543
+new guess is  4.555220997683307
+new guess is  4.555743265552239
+new guess is  4.555398830243649
+new guess is  4.555625974816275
+new guess is  4.555476175432173
+new guess is  4.555574964557791
+new guess is  4.555509814636753
+new guess is  4.555552779647764
+new guess is  4.555524444961165
+new guess is  4.555543131130589
+new guess is  4.555530807938518
+new guess is  4.555538934848503
+;; => 4.555538934848503  
+)
+
+;; with average damping
+(comment
+(defn average [x y] (/ (+ x y) 2.0))
+(fixed-point #(average % (/ (Math/log 1000) (Math/log %))) 1.1)
+new guess is  36.78828689214517
+new guess is  19.352175531882512
+new guess is  10.84183367957568
+new guess is  6.870048352141772
+new guess is  5.227224961967156
+new guess is  4.701960195159289
+new guess is  4.582196773201124
+new guess is  4.560134229703681
+new guess is  4.5563204194309606
+new guess is  4.555669361784037
+new guess is  4.555558462975639
+new guess is  4.55553957996306
+new guess is  4.555536364911781
+;; => 4.555536364911781  
+)
+
+(comment
+"As we can see, average damping significantly reduces the number of steps."
+)
\ No newline at end of file