From: Ramakrishnan Muthukrishnan Date: Sat, 12 Jun 2010 21:02:28 +0000 (+0530) Subject: solutions to 2.12 and 2.13 X-Git-Url: https://git.rkrishnan.org/components/com_hotproperty/frontends/architecture.txt?a=commitdiff_plain;h=c9fa122cefd2bb4ed53b91d66ef1900ea876a0e9;p=sicp.git solutions to 2.12 and 2.13 --- diff --git a/src/sicp/ch2_1.clj b/src/sicp/ch2_1.clj index 9063e98..df583a4 100644 --- a/src/sicp/ch2_1.clj +++ b/src/sicp/ch2_1.clj @@ -2,6 +2,8 @@ (:use [sicp utils] [clojure.contrib test-is])) + +;; 2.1.1 (declare make-rat numer denom) (defn add-rat [x y] @@ -40,4 +42,19 @@ (first (rest x))) (defn print-rat [x] - (println (numer x)"/"(denom x))) \ No newline at end of file + (println (numer x)"/"(denom x))) + +;;; 2.1.3 +;; scheme/CL cons is nothing but a way to represent a pair. +(defn s-cons [x y] + (fn [m] (cond (= m 0) x + (= m 1) y + :else (str "argument not 0 or 1 - s-cons")))) + +(defn car [z] (z 0)) + +(defn cdr [z] (z 1)) + +(def x (s-cons 2 3)) +(car x) ;;=> 2 +(cdr x) ;;=> 3 \ No newline at end of file diff --git a/src/sicp/ch2_1_extended.clj b/src/sicp/ch2_1_extended.clj index 07e6790..399b662 100644 --- a/src/sicp/ch2_1_extended.clj +++ b/src/sicp/ch2_1_extended.clj @@ -23,3 +23,12 @@ (/ 1.0 (lower-bound y))))) +;; provide new constructors +(defn make-center-width [c w] + (make-interval (- c w) (+ c w))) + +(defn center [i] + (/ (+ (lower-bound i) (upper-bound i)) 2)) + +(defn width [i] + (/ (- (upper-bound i) (lower-bound i)) 2)) diff --git a/src/sicp/ex2_12.clj b/src/sicp/ex2_12.clj new file mode 100644 index 0000000..9cf9019 --- /dev/null +++ b/src/sicp/ex2_12.clj @@ -0,0 +1,14 @@ +(ns sicp.ex2_12 + (:use [sicp utils ch2_1_extended ex2_7] + [clojure.test])) + +(defn make-center-percent [c p] + (let [u (+ c (* c p 0.01)) + l (- c (* c p 0.01))] + (make-interval l u))) + +(defn percentage [i] + (let [c (center i) + l (lower-bound i) + u (upper-bound i)] + (* (/ (- u c) c) 100))) \ No newline at end of file diff --git a/src/sicp/ex2_13.clj b/src/sicp/ex2_13.clj new file mode 100644 index 0000000..4f45f8a --- /dev/null +++ b/src/sicp/ex2_13.clj @@ -0,0 +1,26 @@ +(ns sicp.ex2_13 + (:use [sicp utils ch2_1_extended ex2_7] + [clojure.test])) +(comment + "let l1 = c1 - t1, + u1 = c1 + t1, + l2 = c2 - t2 and + u2 = c2 + t2. + +Product of two intervals = min (multiples), max (multiples). But since +t1 and t2 are small, we ignore the t1*t2 terms, so the products +p1,p2,p3 and p4 are: + + p1 = c1*c2 - c1*t2 - c2*t1 + p2 = c1*c2 + c1*t2 - c2*t1 + p3 = c1*c2 - c1*t2 + c2*t1 + p4 = c1*c2 + c1*t2 + c2*t1 + +Now, since all numbers are positive, p1 is the min and p4 is the max. +So, percentage tolerance of the product = + (c1t2 + c2t1)/c1c2 * 100 + + But t1 = c1 * p1 and t2 = c2 *p2 + +So, product tolerance is p1 + p2. i.e. sum of individual tolerances." +) \ No newline at end of file diff --git a/src/sicp/ex2_5.clj b/src/sicp/ex2_5.clj index 95a04c3..a380389 100644 --- a/src/sicp/ex2_5.clj +++ b/src/sicp/ex2_5.clj @@ -34,3 +34,4 @@ (= (cdr c3) 0)) (and (= (car c4) 0) (= (cdr c4) 1))))) + \ No newline at end of file