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1.1.scm
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1.1.scm
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;; 1.3
(define (square x) (* x x))
(define (sum-of-squares x y)
(+ (square x) (square y)))
(define (largest-ss x y z)
(cond ((and (>= x z) (>= y z)) (sum-of-squares x y))
((and (>= x y) (>= z y)) (sum-of-squares x z))
(else (sum-of-squares y z))
))
;; 1.4
;; ((if (> b 0) + -) a b) -> (- a b) when b < 0
;; 1.5
;; Normal order will return 0; applicative order will get stuck in an infinite loop
;; 1.6
;; Infinite loop, because of applicative-order.
;; 1.7
(define (average x y)
(/ (+ x y) 2))
(define (improve guess x)
(average guess (/ x guess)))
(define (good-enough? _ guess x)
(< (abs (- (square guess) x)) 0.001))
(define (good-enough2? old-guess guess _)
(< (/ (abs (- old-guess guess)) guess) 0.001))
(define (sqrt-iter old-guess guess x)
(if (good-enough2? old-guess guess x)
guess
(sqrt-iter guess
(improve guess x)
x)))
(define (sqrt1 x)
(sqrt-iter 0.0 1.0 x))
;; (sqrt1 0.00001) -> 0.03, (sqrt 0.00001) -> 0.01
;; 1.8
(define (improve-cube guess x)
(/ (+ (/ x (square guess)) (* 2 guess)) 3))
(define (cbrt-iter old-guess guess x)
(if (good-enough2? old-guess guess x)
guess
(cbrt-iter guess
(improve-cube guess x)
x)))
(define (cbrt x)
(cbrt-iter 0.0 1.0 x))