Sicp Exercise 1.08

Sep 29, 2015

—

in Functional Programming, Scheme, Sicp Solutions

Exercise 1.8. Newton’s method for cube roots is based on the fact that if y is an approximation to the cube root of x, then a better approximation is given by the value

Use this formula to implement a cube-root procedure analogous to the square-root procedure. (In section 1.3.4 we will see how to implement Newton’s method in general as an abstraction of these square-root and cube-root procedures.)

Solution



	(define (square x) (* x x))

	(define (cube x) (* (* x x) x))

	(define
	(average x y)
	(/
	(+ x y)
	2))

	(define
	(good-enough?
	x
	guess)
	(<
	(abs
	(-
	x
	(square guess)))
	0.00001))

	(define
	(good-enough2?
	x
	guess)
	(<
	(abs
	(-
	x
	guess))
	0.00001))

	(define (abs x)
	(cond ((> x 0) x)
	((= x 0) 0)
	((< x 0) (- x))))

	(define
	(improve-guess
	x
	guess)
	(/
	(+
	(/
	x
	(square guess))
	(* 2 guess))
	3))

	(define
	(cube-iter x guess)

	(if
	(or
	(good-enough?
	x
	guess)
	(good-enough2?
	guess
	(improve-guess
	x
	guess)))

	guess

	(cube-iter
	x
	(improve-guess
	x
	guess)))))


	(define (cube-root x) (cube-iter x 1.0))

view raw

Cuberoot.scm

hosted with ❤ by GitHub

Sicp Exercise 1.08

Share this:

Like this:

Comments

Leave a ReplyCancel reply

Discover more from Gaurav Sharma's Blog