【SICP练习】144 练习3.82

练习3-82

原文

Exercise 3.82. Redo exercise 3.5 on Monte Carlo integration in terms of streams. The stream version of estimate-integral will not have an argument telling how many trials to perform. Instead, it will produce a stream of estimates based on successively more trials.

代码

 (define (random-in-range low high) (let ((range (- high low))) (+ low (* (random) range)))) 
 (define (random-number-pairs low1 high1 low2 high2) (cons-stream (cons (random-in-range low1 high1) (random-in-range low2 high2)) (random-number-pairs low1 high1 low2 high2))) 

 (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 (estimate-integral p x1 x2 y1 y2) (let ((area (* (- x2 x1) (- y2 y1))) (randoms (random-number-pairs x1 x2 y1 y2))) (scale-stream (monte-carlo (stream-map p randoms) 0 0) area))) 

 (define (sum-of-square x y) (+ (* x x) (* y y))) 
 (define f (lambda (x) (not (> (sum-of-square (- (car x) 1) (- (cdr x) 1)) 1)))) 
 (define pi-stream (estimate-integral f 0 2 0 2)) 

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