sicp每日一题[2.5]

Exercise 2.5

Show that we can represent pairs of nonnegative integers using only numbers and arithmetic operations if we represent the pair a and b as the integer that is the product 2^a3b. Give the corresponding definitions of the procedures cons, car, and cdr.

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这道题目难度也不大，只要实现一个辅助函数来计算结果中包含了几个 base 的乘积即可。

; 计算 n 中最多包含几个 base 的积
(define (get-power n base)
  (define (iter k last)
    (if (= (remainder last base) 0)      ; 如果余数为0，说明能够被base整除，则次数 +1
        (iter (+ k 1) (/ last base))
        k))
  (iter 0 n))

(define (cons a b)
  (* (expt 2 a) (expt 3 b)))

(define (car z)
  (get-power z 2))

(define (cdr z)
  (get-power z 3))


(define p (cons 3 2))
(display p)
(newline)
(car p)
(cdr p)

; 执行结果
72
3
2