Add implementation of exercise 3-63 and 3-64

Author: ramsayleung

README.org

@@ -25,7 +25,7 @@
   习题完成情况:
   - 章节一: 43/46
   - 章节二: 88/97
-  - 章节三: 58/82
+  - 章节三: 60/82
   - 章节四: TODO
   - 章节五: TODO
 * 运行

chapter3/exercise3-63.org

@@ -0,0 +1,35 @@
+#+LATEX_CLASS: ramsay-org-article
+#+LATEX_CLASS_OPTIONS: [oneside,A4paper,12pt]
+#+AUTHOR: Ramsay Leung
+#+EMAIL: [email protected]
+#+DATE: 2025-07-29 Tue 23:44
+
+原始版本:
+
+#+begin_src scheme
+  (define (sqrt-stream x)
+    (let ((guesses (cons-stream 
+                    1.0
+                    (stream-map (lambda (guess)
+                                  (sqrt-improve guess x))
+                                guesses))))
+      guesses))
+#+end_src
+
+Louis 的简单版本:
+
+#+begin_src scheme
+  (define (sqrt-stream x)
+    (cons-stream
+     1.0
+     (stream-map (lambda (guess)
+                   (sqrt-improve guess x))
+                 (sqrt-stream x))))
+#+end_src
+
+两者最大的区别就是原始版本有局部变量 =guesses=, 被定义后就在整个流中共享，这意味着每个值只好被计算一次，所以原始版本的时间复杂度是 =O(N)=
+
+而 Louis 版本每次创建流都需要递归访问 =sqrt-stream=, 就需要每次创建流，也就意味着计算第 =n= 个元素就需要重新计算前 =n-1= 个元素，这与未优化的 =fibs= 数列一样，时间复杂度是 =O(2^N)=
+
+无 =memo-proc= 优化的话，原始版本依然高效，因为都指向同一个流，时间复杂度还是 =O(N)=; 而 Louis 版本效率会更差，还会重复计算，依然是指数级，但是效率更差。
+

chapter3/exercise3-64.rkt

@@ -0,0 +1,28 @@
+#lang racket
+(require "stream.rkt")
+(require "iteration-stream.rkt")
+
+(define (stream-limit s tolerance)
+  (if (or (stream-null? s) (stream-null? (stream-cdr s)))
+      (error "The given stream contains less than 2 consecutive items " s)
+      (let ((first (stream-car s))
+            (second (stream-car (stream-cdr s))))
+        (if (<= (abs (- first second)) tolerance)
+            second
+            (stream-limit (stream-cdr s) tolerance)))))
+
+(define (sqrt x tolerance)
+  (stream-limit (sqrt-stream x) tolerance))
+
+(module+ test
+  (require rackunit)
+
+  (test-case "Test for stream-limit"
+             (check-equal? (sqrt 2 0.5) 1.5)
+             (check-equal? (sqrt 2 0.1) 1.4166666666666665)
+                           (check-equal? (sqrt 2 0.01) 1.4142156862745097)
+                           (check-equal? (sqrt 2 0.0001) 1.4142135623746899)
+                           (check-equal? (sqrt 2 0.0000000001) 1.414213562373095)
+                           (check-equal? (sqrt 4 0) 2.0)
+                           )
+  )

chapter3/iteration-stream.rkt

@@ -0,0 +1,18 @@
+#lang racket
+(require "stream.rkt")
+
+(define (average x y)
+  (/ (+ x y) 2))
+
+(define (sqrt-improve guess x)
+  (average guess (/ x guess)))
+
+(define (sqrt-stream x)
+  (define guesses
+    (cons-stream 1.0
+                 (stream-map (λ (guess)
+                               (sqrt-improve guess x))
+                             guesses)))
+  guesses)
+
+(provide sqrt-stream)