Complete up to 3.82

streams.rkt

@@ -836,4 +836,51 @@
     rand)
 
   ;; Test with (define req (make-stream  '(generate generate (reset 19) generate)))
+
+  ;; 3.82
+  ;; Accumulate stream to give a running total
+  (define (stream-acc input)
+    (define acc
+      (cons-stream (stream-car input)
+                   (add-streams acc
+                                (stream-cdr input))))
+    acc)
+
+  ;; Scale stream of random numbers to lie in [low,high]
+  (define (random-stream-in-range low high)
+    (define ones (cons-stream 1 ones))
+    (define (random-stream)
+      (cons-stream (random (- high low))
+                   (random-stream)))
+    (add-streams (scale-stream ones low)
+                 (random-stream)))
+
+  ;; A procedure that generates a stream of booleans:
+  ;; Does a random element from [-1,1]x[-1,1] lie in the cirle
+  ;; of radius 1 centred at (0, 0).
+  ;; P(in circle) = pi*1^2 / 4 = pi/4
+  (define in-circle-test
+    (lambda ()
+      (define (in-circle? radius)
+        (lambda (x y)
+          (<= (+ (* x x) (* y y))
+              (* radius radius))))
+      (let ((radius 1)
+            (x (random-stream-in-range -1.0 1.0))
+            (y (random-stream-in-range -1.0 1.0)))
+        (stream-map (in-circle? radius) x y))))
+  
+  (define (monte-carlo experiment-stream)
+    (define num-trials integers)
+    (define num-trials-passed
+      (stream-acc (stream-map (lambda (x) (if x 1 0)) experiment-stream)))
+    (div-streams num-trials-passed num-trials))
+  
+  ;; Area of circle is pi/r^2.  Area of square is 2*2 = 4
+  ;; So calculated probability is pi/4.
+  (define estimate-pi
+    (scale-stream (monte-carlo (in-circle-test)) 4.0))
+
   )
+
+