Add implementation of exercise 3-55 and 3-56

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: 55/82
+  - 章节三: 57/82
   - 章节四: TODO
   - 章节五: TODO
 * 运行

chapter3/exercise3-56.rkt

@@ -0,0 +1,35 @@
+#lang racket
+(require "stream.rkt")
+(require "infinite-stream.rkt")
+
+;;; 合并排序
+(define (merge s1 s2)
+  (cond ((stream-null? s1) s2)
+        ((stream-null? s2) s1)
+        (else
+         (let ((s1car (stream-car s1))
+               (s2car (stream-car s2)))
+           (cond ((< s1car s2car)
+                  (cons-stream s1car (merge (stream-cdr s1) s2)))
+                 ((< s2car s1car)
+                  (cons-stream s2car (merge s1 (stream-cdr s2))))
+                 (else
+                  ;; s1car = s2car
+                  (cons-stream s1car
+                               (merge (stream-cdr s1)
+                                      (stream-cdr s2)))))))))
+
+(define S (cons-stream 1 (merge (scale-stream S 2) (merge (scale-stream S 3) (scale-stream S 5)))))
+(module+ test
+  (require rackunit)
+
+  (test-case "Test for merge"
+             (define s1 (list-to-stream '(1 2 3 5 7)))
+             (define s2 (list-to-stream '(2 4 5 8 9)))
+             (define s3 (merge s1 s2))
+             (check-equal? (stream-to-list s3 10) '(1 2 3 4 5 7 8 9))
+             )
+  (test-case "Test for S"
+             (check-equal? (stream-to-list S 20) '(1 2 3 4 5 6 8 9 10 12 15 16 18 20 24 25 27 30 32 36))
+             )
+  )

chapter3/exercise3-57.org

@@ -0,0 +1,9 @@
+#+LATEX_CLASS: ramsay-org-article
+#+LATEX_CLASS_OPTIONS: [oneside,A4paper,12pt]
+#+AUTHOR: Ramsay Leung
+#+EMAIL: [email protected]
+#+DATE: 2025-07-28 Mon 21:32
+
+使用 memoization 的做法相当于保证 =fib(k)= 每个数 =k= 只会被计算一次，这个就是动态规划的雏形了。
+
+如果不加 memo，时间复杂度就会变成 =2^n=，有大量的数被重复计算了。

chapter3/infinite-stream.rkt

@@ -26,7 +26,10 @@
 (define (add-streams s1 s2)
   (map-stream + s1 s2))
 
-(provide add-streams ones integers fibs)
+(define (scale-stream stream factor)
+  (stream-map (lambda (x) (* x factor)) stream))
+
+(provide add-streams scale-stream ones integers fibs)
 
 (module+ test
   (require rackunit)