From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
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/pf/content/en/seg/about/statistics?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