Add implementation of exercise 3-81

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: 70/82
+  - 章节三: 71/82
   - 章节四: TODO
   - 章节五: TODO
 * 运行
@@ -121,7 +121,7 @@
 
      当直接计算π困难时，可通过概率实验间接逼近。
 
-     这里利用了数论中的概率规律，将π与随机事件联系起来。(对于高数也只是低分飘过的我来说，不知道数论的东西也太正常了)
+     这里利用了数论中的概率规律，将π与随机事件联系起来。(高数对于我来说已是雪泥鸿爪，更遑论数论的知识了)
 
      #+begin_src racket
        #lang racket

chapter3/exercise3-81.rkt

@@ -0,0 +1,38 @@
+#lang racket
+(require "stream.rkt")
+(require "rand.rkt")
+
+(define (random-stream requests seed)
+  (if (stream-null? requests)
+      the-empty-stream
+      (let ((request (stream-car requests))
+            (rest-requests (stream-cdr requests)))
+
+        (cond ((eq? 'generate request)
+               (let ((next-random (rand-update seed)))
+                 (cons-stream next-random
+                              (random-stream rest-requests next-random))))
+
+              ((and (pair? request) (eq? 'reset (car request)))
+               (let ((new-seed (cadr request)))
+                 (random-stream rest-requests new-seed)))
+
+              (else
+               (random-stream rest-requests seed))))))
+
+(module+ test
+  (require rackunit)
+
+  (test-case "Test for random-stream"
+             (define requests (list-to-stream '(generate
+                                                generate
+                                                generate
+                                                (reset 42)
+                                                generate
+                                                generate
+                                                generate
+                                                generate)))
+             (define random-numbers (random-stream requests 42))
+             (check-equal? (stream-take-n random-numbers 8) '(2027382 1226992407 551494037 2027382 1226992407 551494037 961371815))
+             )
+  )

chapter3/infinite-stream.rkt

@@ -1,6 +1,7 @@
 #lang racket
 (require "stream.rkt")
 (require "exercise3-50.rkt")
+(require "rand.rkt")
 
 (define (integers-starting-from n)
   (cons-stream n (integers-starting-from (+ n 1))))
@@ -52,7 +53,38 @@
                               int)))
   int)
 
-(provide add-streams scale-stream ones integers fibs interleave pairs integral)
+(define random-number-stream
+  (cons-stream random-init
+               (stream-map rand-update random-number-stream)))
+
+(define (map-successive-pairs f s)
+  (cons-stream
+   (f (stream-car s) (stream-car (stream-cdr s)))
+   (map-successive-pairs f (stream-cdr (stream-cdr s)))))
+
+(define cesaro-stream
+  (map-successive-pairs (lambda (r1 r2) (= (gcd r1 r2) 1))
+                        random-number-stream))
+
+(define (monte-carlo experiment-stream passed failed)
+  (define (next passed failed)
+    (cons-stream
+     (/ passed (+ passed failed))
+     (monte-carlo
+      (stream-cdr experiment-stream)
+      passed
+      failed)))
+  (if (stream-car experiment-stream)
+      (next (+ passed 1) failed)
+      (next passed (+ failed 1))))
+
+(define pi-stream
+  (stream-map (lambda (p) (sqrt (/ 6 p)))
+              ;; bypass division by zero problem
+              (stream-filter (lambda (p) (not (= p 0)))
+                             (monte-carlo cesaro-stream 0 0))))
+
+(provide add-streams scale-stream ones integers fibs interleave pairs integral monte-carlo)
 
 (module+ test
   (require rackunit)

chapter3/rand.rkt

@@ -21,6 +21,8 @@
   (let ((range (- high low)))
     (+ low (random range))))
 
+(provide random-init rand-update)
+
 (module+ test
   (require rackunit)
   (require rackunit/text-ui)