# sicp-ex-3.82

meteorgan

```

(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)))

;; test. get the value of pi
(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))
```

tango

Meteorgan's solution uses the monte-carlo method with variables 'passed' and 'failed'. Following solution doesn't uses these and relies solely on streams.

```
(define (add-streams s1 s2) (stream-map + s1 s2))
(define ones (cons-stream 1.0 ones))
(define integers (cons-stream 1.0 (add-streams ones integers)))

(define (random-stream lo hi)
(define (random-in-range low high)
(let ((range (- high low)))
(+ low (random range))))
(cons-stream (random-in-range lo hi) (random-stream lo hi)))

(define (estimate-integral p x1 x2 y1 y2)
(define throw-results (stream-map (lambda (x) (if (eq? x true) 1.0 0))
(stream-map p (random-stream x1 x2) (random-stream y1 y2))))
(define succesful-throws
(cons-stream (stream-car throw-results) (add-streams (stream-cdr throw-results) succesful-throws)))
(define (get-area probability) (* probability (abs (* (- y2 y1) (- x2 x1)))))
(stream-map get-area (stream-map / succesful-throws integers)))
```

master

Isn't producing random numbers the predicate's job? Doesn't the following simple definition of estimate-integral suffice?

``` (define (estimate-integral P x1 x2 y1 y2)
(let ((width (- x2 x1))
(height (- y2 y1)))
(let ((area (* width height)))
(scale-stream (monte-carlo P 0 0) area))))
```