Add implementation of exercise 3-70

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: 63/82
+  - 章节三: 64/82
   - 章节四: TODO
   - 章节五: TODO
 * 运行
@@ -144,4 +144,18 @@
      #+end_src
 
      这里的蒙特卡罗实现真的是优雅
-     
+*** 翻译错误
+    第2版，238页，模块化，对象和状态，中文翻译是
+    #+begin_quote
+    练习3.70
+    b) 所有正正数序对 (i,j) 的流，其中要求 i<=j, 而且这里的i或者j可以被2,3或者5整除
+    #+end_quote
+
+    原文是:
+    #+begin_quote
+    the stream of all pairs of positive integers ( i , j ) with i ≤ j , where neither i nor j is divisible by 2, 3, or 5,
+    #+end_quote
+
+    https://sarabander.github.io/sicp/html/3_002e5.xhtml#g_t3_002e5
+    
+    i和j不可以被2,3,5整除，翻译成了可以被2,3或者5整除，意义完全相反，真的是服了。

chapter3/exercise3-70.rkt

@@ -0,0 +1,65 @@
+#lang racket
+(require "stream.rkt")
+(require "infinite-stream.rkt")
+
+(define (merge-weighted s1 s2 weight)
+  (cond ((stream-null? s1) s2)
+        ((stream-null? s2) s1)
+        (else
+         (let* ((s1-head (stream-car s1))
+                (s2-head (stream-car s2))
+                (w1 (weight s1-head))
+                (w2 (weight s2-head)))
+           (cond ((<= w1 w2)
+                  (cons-stream s1-head (merge-weighted (stream-cdr s1) s2 weight)))
+                 (else
+                  (cons-stream s2-head (merge-weighted s1 (stream-cdr s2) weight))))))))
+
+(define (pairs-weighted s t weight)
+  (if (or (stream-null? s)
+          (stream-null? t))
+      the-empty-stream
+      (cons-stream
+       (list (stream-car s) (stream-car t))
+       (merge-weighted
+        (stream-map (lambda (x) (list (stream-car s) x))
+                    (stream-cdr t))
+        (pairs-weighted (stream-cdr s) (stream-cdr t) weight)
+        weight))))
+
+(module+ test
+  (require rackunit)
+
+  (define not-div-by-2-3-5
+    (stream-filter
+     (lambda (x)
+       (not (or (= (remainder x 2) 0)
+                (= (remainder x 3) 0)
+                (= (remainder x 5) 0))))
+     integers))
+
+  (test-case "Test for merge-weighted"
+             (define s1 (list-to-stream '(1 2 3 5 7)))
+             (define s2 (list-to-stream '(2 -4 5 8 9)))
+             (define weight (lambda (x) (abs x)))
+             (define s3 (merge-weighted s1 s2 weight))
+             (check-equal? (stream-to-list s3 10) '(1 2 2 3 -4 5 5 7 8 9))
+             )
+
+  (test-case "Test for pairs-weighted with weight = i+j"
+             (define s1 (list-to-stream '(1 2 3)))
+             (define s2 (list-to-stream '(1 2 3)))
+             (define weight (lambda (pair) (+ (car pair) (cadr pair))))
+             (define s3 (pairs-weighted s1 s2 weight))
+             (check-equal? (stream-to-list s3 10) '((1 1) (1 2) (1 3) (2 2) (2 3) (3 3)))
+             )
+
+  (test-case "Test for pairs-weighted with weight = 2j + 3j + 5ij"
+             (define weight (lambda (pair) (let ((i (car pair))
+                                                 (j (cadr pair)))
+                                             (+ (* 2 i)
+                                                (* 3 j)
+                                                (* 5 i j)))))
+             (define result (pairs-weighted not-div-by-2-3-5 not-div-by-2-3-5 weight))
+             (check-equal? (stream-to-list result 5) '((1 1) (1 7) (1 11) (1 13) (1 17))))
+  )