solution to 1.45

diff --git a/src/sicp/ex1_45.clj b/src/sicp/ex1_45.clj
new file mode 100644 (file)
index 0000000..cf077d9
--- /dev/null
+++ b/src/sicp/ex1_45.clj
@@ -0,0 +1,60 @@
+(ns sicp.ex1_45
+  (:use [clojure.contrib test-is]
+       [sicp utils]
+       [sicp ch1_3]
+       [sicp ex1_43]))
+
+(defn nthroot [x n]
+  (fixed-point ((repeated average-damp
+                         (int (/ (Math/log n) (Math/log 2)))) 
+               (fn [y] (/ x (Math/pow y (- n 1)))))
+              1.0))
+
+;; experiments show that average damp needs to e applied log2n times.
+(comment
+user> (nthroot (* 3 3 3) 3)
+;;=> 2.9999972321057697
+user> (nthroot (* 3 3 3 3) 4)
+; Evaluation aborted.
+user> (use 'sicp.ex1_45 :reload)
+;;=> nil
+user> (nthroot (* 3 3 3 3) 4)
+;;=> 3.000000000000033
+user> (nthroot (* 3 3 3 3 3) 5)
+;;=> 3.0000008877496294
+user> (nthroot (* 3 3 3 3 3 3) 5)
+;;=> 3.737194011460545
+user> (nthroot (* 3 3 3 3 3 3) 6)
+;;=> 2.999996785898161
+user> (nthroot (* 3 3 3 3 3 3 3) 7)
+;;=> 3.0000041735235947
+user> (nthroot (* 3 3 3 3 3 3 3 3) 8)
+;;=> ; Evaluation aborted.
+user> (use 'sicp.ex1_45 :reload)
+;;=> nil
+user> (nthroot (* 3 3 3 3 3 3 3 3) 8)
+;;=> 3.0000000000173292
+user> (nthroot (* 3 3 3 3 3 3 3 3 3 3 3 3 3 3) 14)
+;;=> 2.9999959148601363
+user> (nthroot (* 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3) 15)
+;;=> 3.000004202219401
+user> (nthroot (* 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3) 16)
+;;=> ; Evaluation aborted.
+user> (Math/log2 10)
+;;=> ; Evaluation aborted.
+user> (/ (Math/log 10) (Math/log 2))
+;;=> 3.3219280948873626
+user> (/ (Math/log 16) (Math/log 2))
+;;=> 4.0
+user> (use 'sicp.ex1_45 :reload)
+;;=> nil
+user> (nthroot (* 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3) 16)
+;;=> 3.0
+user> (nthroot (Math/pow 3 16) 16)
+;;=> 3.0
+user> (nthroot (Math/pow 3 35) 35)
+;;=> 3.000000146591681
+user> (nthroot (Math/pow 3 50) 50)
+;;=> 2.9999967255008917
+user>   
+)
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