Middle Earth

sicp-exercise-1.44-1.46

Exercise 1.44


(define (average a b c) ;there should be a general way to get average
  (/ (+ a b c) 3.0))

(define (smooth f)
  (lambda (x)
    (average (f x)
             (f (- x 0.5))
             (f (+ x 0.5)))))

(define (n-fold-smooth f n)
    (repeated (smooth f) n))
I need to check my answer through some examples, will find some later.

Exercise 1.45

(define (nth-root x n damp-times)
  (find-fixed-points ((repeated average-damp (damp-times n))
                      (lambda (y) (/ x (fast-expt y (- n 1)))))
                     1.0))

damp time should be n/2
(define (half n) (/ n 2))
But how to cast n to integer, in case I receive a float number?

And yet, it doesn’t work that well:
;1 ]=> (nth-root 32 5 half)
;Aborting!: out of memory

Exercise 1.46

iterative-improve return a procedure built from its two parameters good-enough? and improve-guess. The returned procedure iteratively improves the guess until good enough.

(define (iterative-improve good-enough? improve-guess)
  (define (get-guess guess)
    (if (good-enough? guess)
      guess
      (get-guess (improve-guess guess))))
  get-guess)


(define (iter-improve-sqrt x)
  ((iterative-improve (lambda (guess)
                       (< (abs (- (square guess) x))
                          0.01))
                      (average-damp (lambda (y) (/ x y))))
   1.0))

(define (close-enough? v1 v2)
  (< (abs (- v1 v2)) 0.00001))

(define (iter-improve-fixed-point f first-guess)
  ((iterative-improve (lambda (guess) (close-enough? guess (f guess)))
                      (lambda (guess) (f guess)))
   first-guess))

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