From 8b52e1f31c0570c4180f1772f9d1226d349be37c Mon Sep 17 00:00:00 2001
From: Ramakrishnan Muthukrishnan <vu3rdd@gmail.com>
Date: Thu, 28 Jul 2011 22:25:28 +0530
Subject: [PATCH] solutions to 3.64, 3.65, 3.66, 3.67, 3.68 and 3.69

---
 src/sicp/ex3_64.rkt | 10 ++++++++++
 src/sicp/ex3_65.rkt |  7 +++++++
 src/sicp/ex3_66.rkt | 14 ++++++++++++++
 src/sicp/ex3_67.rkt | 22 ++++++++++++++++++++++
 src/sicp/ex3_68.rkt |  9 +++++++++
 src/sicp/ex3_69.rkt | 11 +++++++++++
 6 files changed, 73 insertions(+)
 create mode 100644 src/sicp/ex3_64.rkt
 create mode 100644 src/sicp/ex3_65.rkt
 create mode 100644 src/sicp/ex3_66.rkt
 create mode 100644 src/sicp/ex3_67.rkt
 create mode 100644 src/sicp/ex3_68.rkt
 create mode 100644 src/sicp/ex3_69.rkt

diff --git a/src/sicp/ex3_64.rkt b/src/sicp/ex3_64.rkt
new file mode 100644
index 0000000..19f5d15
--- /dev/null
+++ b/src/sicp/ex3_64.rkt
@@ -0,0 +1,10 @@
+#lang planet neil/sicp
+
+;; stream-of-numbers -> floating point number -> number
+(define (stream-limit s limit)
+  (let ([num0 (stream-car s)]
+        [num1 (stream-car (stream-cdr s))])
+    (let ([diff (- num0 num1)])
+      (if (< (abs diff) limit)
+          num1
+          (stream-limit (stream-cdr s) limit)))))
\ No newline at end of file
diff --git a/src/sicp/ex3_65.rkt b/src/sicp/ex3_65.rkt
new file mode 100644
index 0000000..7d5be8a
--- /dev/null
+++ b/src/sicp/ex3_65.rkt
@@ -0,0 +1,7 @@
+#lang racket
+
+(define (ln2-summands n)
+  (cons-stream (/ 1.0 n)
+               (stream-map - (ln2-summands (+ n 1)))))
+
+(define ln2 (partial-sums (ln2-summands 1)))
\ No newline at end of file
diff --git a/src/sicp/ex3_66.rkt b/src/sicp/ex3_66.rkt
new file mode 100644
index 0000000..530b289
--- /dev/null
+++ b/src/sicp/ex3_66.rkt
@@ -0,0 +1,14 @@
+#lang racket
+
+#|
+
+Writing down the pairs, one can sort of form the following judgement.
+
+For any particular pair of the form S0Tm, the number of terms which precedes it
+is (+ (* 2 (- m 1)) 1) for m >= 2
+
+For a pair of the form S1Tm, it is (* (- m 1) 4) for m >= 2.
+
+Similarly one can get working formulae for other row, column pairs.
+
+|#
\ No newline at end of file
diff --git a/src/sicp/ex3_67.rkt b/src/sicp/ex3_67.rkt
new file mode 100644
index 0000000..7a32c7e
--- /dev/null
+++ b/src/sicp/ex3_67.rkt
@@ -0,0 +1,22 @@
+#lang racket
+
+(define (interleave s1 s2)
+  (if (stream-null? s1)
+      s2
+      (cons-stream (stream-car s1)
+                   (interleave s2 (stream-cdr s1)))))
+
+(define (pairs s t)
+  (cons-stream
+   (list (stream-car s) (stream-car t))
+   (interleave (interleave
+                (stream-map (lambda (x) (list (stream-car s) x))
+                            (stream-cdr t))
+                (stream-map (lambda (y) (list y (stream-car t)))
+                            (stream-cdr s)))                
+               (pairs (stream-cdr s) (stream-cdr t)))))
+
+                              
+               
+
+
diff --git a/src/sicp/ex3_68.rkt b/src/sicp/ex3_68.rkt
new file mode 100644
index 0000000..4af41dc
--- /dev/null
+++ b/src/sicp/ex3_68.rkt
@@ -0,0 +1,9 @@
+#lang racket
+
+#|
+
+'interleave' is a procedure and not a special form because of which the arguments
+of the interleave will be evaluated before interleave itself is called. This will
+result in an infinite number of calls to 'pair'.
+
+|#
\ No newline at end of file
diff --git a/src/sicp/ex3_69.rkt b/src/sicp/ex3_69.rkt
new file mode 100644
index 0000000..6b0905e
--- /dev/null
+++ b/src/sicp/ex3_69.rkt
@@ -0,0 +1,11 @@
+#lang racket
+
+(define (triples s t u)
+  (cons-stream (append (stream-car (pairs s t))
+                       (list (stream-car u)))
+               (interleave
+                (stream-map (lambda(p) (append p (list (stream-car u))))
+                            (stream-cdr (pairs s t)))
+                (triples (stream-cdr s)
+                         (stream-cdr t)
+                         (stream-cdr u)))))
\ No newline at end of file
-- 
2.37.2