sicp练习1.18 基于加法、加倍和折半运算求两个整数之乘积

;double的功能是2*n
(define (double n)
  (+ n n))

(double 5)

;havle-iter函数的功能是通过迭代获得n的一半的值,guess是初始猜测值
(define (havle-iter guess n)
  (cond ((not (integer? n)) (display "error: 原因havle函数的参数是整数\n"))
        (( and (< (double guess) n) (<= (double (+ guess 1)) n)) (havle-iter (+ 1 guess) n))
        (( and (> (double guess) n)) (havle-iter (- guess 1) n))
        (( and (< (double guess) n) (> (double (+ guess 1)) n)) (+ guess 0.5))
        ((= (double guess) n) guess)))
;havle函数的功能是通过迭代获得n的一半的值,guess是初始猜测值是1
(define (halve n)
  (havle-iter 1 n))

(halve 16)

(halve 37)

(halve 35.5)

;even?函数功能是判断n是否是偶数,如果是偶数值为#t,否则为#f
(define (even? n)
  (cond ((= n 0) #t)
        ((= n 1) #f)
        ((and (integer? n) (< n 0)) (even? (+ n 2)))
        ((and (integer? n) (> n 1)) (even? (- n 2)))
        (else #f)))

(even? 13)

(even? 22)

(even? 22.5)

;*函数的功能是a乘以b
(define (* a b)
  (cond ((or (= a 0) (= b 0)) 0)
        ((= a 1) b)
        ((even? a) (* (halve a) (double b)))
        (else (+ (* (- a 1) (- b 1)) a b -1))))

(* 3 4)