From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Sun, 17 Jun 2012 12:43:15 +0000 (+0530)
Subject: solutions to 4.35, 4.36 and 4.37
X-Git-Url: https://git.rkrishnan.org/pf/content/en/seg/%22news.html/index.php?a=commitdiff_plain;h=16ffd75b36a5dbfbda3da703c2732f8f49208c11;p=sicp.git

solutions to 4.35, 4.36 and 4.37
---

diff --git a/src/sicp/amb-eli.rkt b/src/sicp/amb-eli.rkt
new file mode 100644
index 0000000..737fd82
--- /dev/null
+++ b/src/sicp/amb-eli.rkt
@@ -0,0 +1,42 @@
+#lang racket
+(provide amb assert)
+
+(define failures null)
+
+(define (fail)
+  (if (pair? failures)
+      ((first failures))
+      (error "no more choices!")))
+
+(define (amb/thunks choices)
+  (let/cc k (set! failures (cons k failures)))
+  (if (pair? choices)
+      (let ([choice (first choices)])
+        (set! choices (rest choices))
+        (choice))
+      (begin (set! failures (rest failures))
+             (fail))))
+
+(define-syntax-rule (amb E ...)
+  (amb/thunks (list (lambda () E) ...)))
+
+(define (assert condition)
+  (unless condition (fail)))
+
+(define (collect/thunk n thunk)
+  (define results null)
+  (let/cc too-few
+    (set! failures (list too-few))
+    (define result (thunk))
+    (set! results (cons result results))
+    (set! n (sub1 n))
+    (unless (zero? n) (fail)))
+  (set! failures null)
+  (reverse results))
+
+(define-syntax collect
+  (syntax-rules ()
+    ;; collect N results
+    [(_ N E) (collect/thunk N (lambda () E))]
+    ;; collect all results
+    [(_ E) (collect/thunk -1 (lambda () E))]))
diff --git a/src/sicp/ex4_35.scm b/src/sicp/ex4_35.scm
new file mode 100644
index 0000000..f1b57da
--- /dev/null
+++ b/src/sicp/ex4_35.scm
@@ -0,0 +1,33 @@
+;; done in Chicken scheme which has a builtin amb operator
+;; - can be installed with
+;;   $ chicken-install amb
+
+(use amb)
+(use srfi-1)
+
+(define (require p)
+  (if (not p) (amb)))
+
+(define (an-element-of items)
+  (require (not (null? items)))
+  (amb (car items) (an-element-of (cdr items))))
+
+(define (an-integer-between low high)
+  (let [(count (- high low))]
+    (let [(items (iota count low))]
+      (an-element-of items))))
+
+(define (a-pythagorean-triple-between low high)
+  (let ((i (an-integer-between low high)))
+    (let ((j (an-integer-between i high)))
+      (let ((k (an-integer-between j high)))
+        (require (= (+ (* i i) (* j j)) (* k k)))
+        (list i j k)))))
+
+;; another implementation
+(define (an-integer-between-2 low high)
+  (require (< low high))
+  (amb low (an-integer-between-2 (+ low 1) high)))
+
+;; play with it
+(a-pythagorean-triple-between 1 20)
diff --git a/src/sicp/ex4_36.rkt b/src/sicp/ex4_36.rkt
new file mode 100644
index 0000000..5c9ec2d
--- /dev/null
+++ b/src/sicp/ex4_36.rkt
@@ -0,0 +1,28 @@
+#lang racket
+
+(require "amb-eli.rkt")
+
+(define (an-integer-starting-from n)
+  (amb n (an-integer-starting-from (+ n 1))))
+
+(define (an-integer-between low high)
+  (assert (< low high))
+  (amb low (an-integer-between (+ low 1) high)))
+
+#|
+
+If we replace an-integer-between with an-integer-starting-from, then
+the k grows too high to invalid ranges and never stops. The way to accomplish
+correct values is to restrict i, j and k to valid ranges.
+
+|#
+
+;; using euclid's formula
+;; http://en.wikipedia.org/wiki/Pythagorean_triple#Generating_a_triple
+(define (pythagorean-triples)
+  (let [(n (an-integer-starting-from 1))]
+    (let [(m (an-integer-starting-from n))]
+      (assert (> m n))
+      (list (- (sqr m) (sqr n))
+            (* 2 m n)
+            (+ (sqr m) (sqr n))))))
\ No newline at end of file
diff --git a/src/sicp/ex4_37.rkt b/src/sicp/ex4_37.rkt
new file mode 100644
index 0000000..a4528a0
--- /dev/null
+++ b/src/sicp/ex4_37.rkt
@@ -0,0 +1,25 @@
+#lang racket
+
+(require "amb-eli.rkt")
+
+(define (a-pythagorean-triple-between low high)
+  (let ((i (an-integer-between low high))
+        (hsq (* high high)))
+    (let ((j (an-integer-between i high)))
+      (let ((ksq (+ (* i i) (* j j))))
+        (assert (>= hsq ksq))
+        (let ((k (sqrt ksq)))
+          (assert (integer? k))
+          (list i j k))))))
+
+#|
+
+Yes, Ben is correct. The above program prunes the search space by restricting the
+possible values of k.
+
+k^2 <= high^2
+
+and sqrt (i^2 + j^2) is an integer. This eliminates a large number of (i, j, k) triples
+and hence the search space is a lot less than the naive implementation in the text.
+
+|#