solutions to 2.12 and 2.13

diff --git a/src/sicp/ch2_1.clj b/src/sicp/ch2_1.clj
index 9063e9846d75aa8e4fed87a65fb90ea910eb16cd..df583a4f150ea8095283d61322cf410ca95180a3 100644 (file)
--- 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 07e67903a72606d40c869bc9ec2b45fe5e1dca59..399b66246a0ef72112ed38b2fc1b7811e6a0ae3e 100644 (file)
--- 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 (file)
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)))
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diff --git a/src/sicp/ex2_13.clj b/src/sicp/ex2_13.clj
new file mode 100644 (file)
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 95a04c3423ef65101dedefc01d10ab1cb09b062a..a3803898bfe9d3eb29d15685131cd38bffb0c6e6 100644 (file)
--- 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