Chapter 3, Modularity, Objects, and State
Exercise 3.5
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#lang sicp
(#%require (only racket/base error))
(define (random-in-range low high)
(let ((range (- high low)))
(+ low (random range))))
(define (square x) (* x x))
(define (estimate-integral pr x1 x2 y1 y2 trials)
(let ((rect-area (* (- x2 x1) (- y2 y1))))
(* (monte-carlo trials pr) rect-area)))
(define (circle-test cx cy r)
(lambda (x y)
(let ((d2 (+ (square (- x cx)) (square (- y cy))))
(r2 (square r)))
(< d2 r2))))
(define (estimate-pi trials)
(let ((x1 -1.0)
(x2 1.0)
(y1 -1.0)
(y2 1.0))
(let ((unit-circle-test
(lambda ()
((circle-test 0.0 0.0 1.0) (random-in-range x1 x2)
(random-in-range y1 y2)))))
(estimate-integral unit-circle-test x1 x2 y1 y2 trials))))
(define (monte-carlo trials experiment)
(define (iter trials-remaining trials-passed)
(cond ((= trials-remaining 0)
(/ trials-passed trials))
((experiment)
(iter (- trials-remaining 1) (+ trials-passed 1)))
(else
(iter (- trials-remaining 1) trials-passed))))
(iter trials 0))
Output:
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> (estimate-pi 100)
2.8
> (estimate-pi 500)
3.128
> (estimate-pi 500)
3.12
> (estimate-pi 1000)
3.104
> (estimate-pi 10000)
3.1248
> (estimate-pi 100000)
3.15444
> (estimate-pi 10000000)
3.1422792
>