Add exercise3-5 and 3-6

Author: ramsayleung

chapter3/exercise3-5.rkt

@@ -0,0 +1,53 @@
+#lang racket
+(require "rand.rkt")
+(require "monte-calro.rkt")
+
+;; 蒙特卡罗积分的思路:
+;; 在矩形内随机生成大量点 (x, y)
+;; 计算满足 P(x, y) 的点的比例, 如半径为3、中心在 (5,7) 的圆，其谓词为
+;; P(x, y) = (x-5) ^2 + (y-7) ^ 2 ≤ 9
+;; 估算圆在矩形内的面积:
+;; 圆的面积 ~= 矩形面积 * 满足p的点 / 总的点数
+
+(define (estimate-integral predicate x1 x2 y1 y2 trials)
+  ;; 判断是否落在圆内
+  (define (experiment)
+    (let ((x (random-in-range x1 x2))
+          (y (random-in-range y1 y2)))
+      (predicate x y)))
+
+  (let ((rectangle-area (* (abs (- x1 x2))
+                           (abs (- y1 y2)))))
+    (* (exact->inexact rectangle-area) (monte-carlo trials experiment))))
+
+(module+ test
+  (require rackunit)
+  (require rackunit/text-ui)
+
+  ;; 以(5,7)为圆心，半径为3的圆，以(2,4)和(8,10)作为对角点的矩形包围着
+  ;; 这个圆, 计算这个圆的面积（假设 π未知），结果应该接近 28.274
+  (define (square x)
+    (* x x))
+
+  (define (in-circle? x y)
+    (<= (+ (square (- x 5)) (square (- y 7)))
+        (square 3)))
+
+  (define (estimate-area-close? trials tolerance)
+    (let ((area-estimate (estimate-integral in-circle? 2 8 4 10 trials)))
+      (< (abs (- area-estimate 28.27431)) tolerance)))
+
+  (define module-test
+    (test-suite
+     "Tests for in-circle?"
+     (check-true (in-circle? 5 6))
+     (check-true (in-circle? 6 5))
+     (check-false (in-circle? 10 10))
+
+     "Tests for estimate-integral"
+     (check-true (estimate-area-close? 10000 2.0))
+     (check-true (estimate-area-close? 100000 1.5))
+     (check-true (estimate-area-close? 10000000 1.3))
+     (check-exn exn:fail? (lambda () (estimate-area-close? 0)) "Should throw exception for 0 trials")
+     ))
+  (run-tests module-test))

chapter3/exercise3-6.rkt

@@ -0,0 +1,40 @@
+#lang racket
+(require "rand.rkt")
+
+(define random-init 42)
+(define rand
+  (let ((x random-init))
+    (lambda (param)
+      (cond ((eq? param 'generate)
+             (set! x (rand-update x))
+             x)
+            ((eq? param 'reset)
+             (lambda (new-value)
+               (set! x new-value)))
+            (else (error "Unknown operation -- RAND" param))))))
+
+(module+ test
+  (require rackunit)
+  (require rackunit/text-ui)
+
+  (define module-test
+    (test-suite
+     "Tests for resetable random generater"
+     (let ((num1 (rand 'generate))
+           (num2 (rand 'generate)))
+       (check-false (= num1 num2)
+                    "Sequential calls should produce different numbers"))
+
+     "Reset functionality"
+     (let ((reset-proc (rand 'reset)))
+       ;; Generate first sequence
+       (reset-proc 42)
+       (let ((seq1 (list (rand 'generate) (rand 'generate) (rand 'generate))))
+
+         ;; Reset and generate second sequence
+         (reset-proc 42)
+         (let ((seq2 (list (rand 'generate) (rand 'generate) (rand 'generate))))
+           (check-equal? seq1 seq2 "Sequences should be identical after same reset"))))
+     ))
+
+  (run-tests module-test))

chapter3/monte-calro.rkt

@@ -32,3 +32,5 @@
      (check-exn exn:fail? (lambda () (estimate-pi 0)) "Should throw exception for 0 trials")
      ))
   (run-tests module-test))
+
+(provide monte-carlo)

chapter3/rand.rkt

@@ -17,4 +17,23 @@
       (set! x (rand-update x))
       x)))
 
-(provide rand)
+(define (random-in-range low high)
+  (let ((range (- high low)))
+    (+ low (random range))))
+
+(module+ test
+  (require rackunit)
+  (require rackunit/text-ui)
+
+  (define module-test
+    (test-suite
+     "Tests for random-in-range"
+     (check-true (andmap (lambda (_) (let ((a (random-in-range 1 10)))
+                                       (and (<= a 10)
+                                            (>= a 1))))
+                         (range 3000)))
+     ))
+
+  (run-tests module-test))
+
+(provide rand random-in-range rand-update)