From: Ramakrishnan Muthukrishnan 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/components/com_hotproperty/%22doc.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)))