From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Thu, 22 Jul 2010 03:42:36 +0000 (+0530)
Subject: solution to 2.29
X-Git-Url: https://git.rkrishnan.org/components/%22news.html/frontends/rgr-080307.php?a=commitdiff_plain;h=645caefa0c3d0cbfa183fbe6c5cc3d7a89640220;p=sicp.git

solution to 2.29
---

diff --git a/src/sicp/ex2_29.clj b/src/sicp/ex2_29.clj
new file mode 100644
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+++ b/src/sicp/ex2_29.clj
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+(ns sicp.ex2_29
+  (:use [clojure.test]))
+
+(defn make-mobile [left right]
+  (list left right))
+
+(defn make-branch [length structure]
+  (list length structure))
+
+;; a.  Write the corresponding selectors left-branch and
+;;     right-branch, which return the branches of a mobile, and
+;;     branch-length and branch-structure, which return the
+;;     components of a branch.
+(defn left-branch [mobile]
+  (first mobile))
+
+(defn right-branch [mobile]
+  (first (rest mobile)))
+
+(defn branch-length [branch]
+  (first branch))
+
+(defn branch-structure [branch]
+  (first (rest branch)))
+
+(deftest test-constructors-selectors
+  (let [m (make-mobile (make-branch 3 8)
+		       (make-branch 9
+				    (make-mobile (make-branch 2 1)
+						 (make-branch 1 2))))]
+    (are [x y] [= x y]
+	 m '((3 8) (9 ((2 1) (1 2))))
+	 (right-branch m) '(9 ((2 1) (1 2)))
+	 (left-branch m) '(3 8)
+	 (branch-length (left-branch m)) 3
+	 (branch-length (right-branch m)) 9
+	 (branch-structure (left-branch m)) 8
+	 (branch-structure (right-branch m)) '((2 1) (1 2)))))
+
+;; b.  Using your selectors, define a procedure total-weight that
+;;     returns the total weight of a mobile.
+
+(declare total-branch-weight)
+
+(defn total-weight [mobile]
+  (+ (total-branch-weight (right-branch mobile))
+     (total-branch-weight (left-branch mobile))))
+
+(defn total-branch-weight [branch]
+  (let [structure (branch-structure branch)]
+    (cond (number? structure) structure
+	  :else (total-weight structure))))
+
+(deftest test-weights
+  (let [m (make-mobile (make-branch 3 8)
+		       (make-branch 9
+				    (make-mobile (make-branch 2 1)
+						 (make-branch 1 2))))]
+    (are [x y] [= x y]
+	 (total-weight m) 11)))
+
+;; c. A mobile is said to be balanced if the torque applied by its
+;;    top-left branch is equal to that applied by its top-right branch
+;;    (that is, if the length of the left rod multiplied by the weight
+;;    hanging from that rod is equal to the corresponding product for
+;;    the right side) and if each of the submobiles hanging off its
+;;    branches is balanced. Design a predicate that tests whether a
+;;    binary mobile is balanced.
+
+(defn torque [branch]
+  (* (branch-length branch) (total-branch-weight branch)))
+
+(defn mobile? [structure]
+  (seq? structure))
+
+(defn balanced? [mobile]
+  (let [lstructure   (branch-structure (left-branch mobile))
+	rstructure   (branch-structure (right-branch mobile))]
+    (and (= (torque (left-branch mobile))
+	    (torque (right-branch mobile)))
+	 (if (mobile? lstructure)
+	   (balanced? lstructure)
+	   true)
+	 (if (mobile? rstructure)
+	   (balanced? rstructure)
+	   true))))
+
+(deftest test-balance
+  (let [m1 (make-mobile (make-branch 3 9)
+			(make-branch 9
+				     (make-mobile (make-branch 2 1)
+						  (make-branch 1 2))))
+	m2 (make-mobile (make-branch 2 4)
+			(make-branch 3
+				     (make-mobile (make-branch 2 1)
+						  (make-branch 4 2))))]
+    (are [x y] [= x y]
+	 (balanced? m1) true
+	 (balanced? m2) false)))
+
+;; d. Suppose we change the representation of mobiles.
+;;    How much do you need to change your programs to convert
+;;    to the new representation?
+
+;; soln
+;; if I were to do it in scheme, then oly selectors would change.
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