sicp练习1.17 只有加减法 实现快速求幂
;double的功能是2*n(define (double n) (+ n n))(double 5);*函数的功能是a乘以b(define (* a b) (if (= b 0) 0 (+ a (* a (- b 1)))))(* 3 4);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);square函数的功能是得到n的平方，如果是非零正偶数则递归计算4倍二分之n的平方(define (square n) (cond ((= n 0) 0) ((< n 0) (square (- 0 n))) ((and (> n 0) (even? n)) (double (double (square (halve n))))) ((> n 0) (+ (square (- n 1)) (double (- n 1)) 1))))(square 7)(square 12)(define (fast-expt b n) (cond ((= 0 n) 1) ((even? n) (fast-expt (square b) (halve n))) (else (* b (fast-expt b (- n 1))))))(fast-expt 2 10)?
