NCNU LISP HW8

exercise 8: Combining three numbers with exponentiation and multiplication

• Refer to exercise 2.5 but the pair is replaced with a triple. That is, the interface functions are :
  (combine a b c), (first x), (second x), (third x)

(define (combine a b c)

  (do-combine a b c 1)

) 

(define (do-combine a b c num)

(if (= a 0)

(if (= b 0)

(if (= c 0) num

           (do-combine a b (- c 1) (* 5 num))

)

   (do-combine a (- b 1) c (* 4 num))

)

   (do-combine (- a 1) b c (* 3 num))

  )

)

(define (first x)

(common x 3)

)

(define (second x)

(common x 4)

)

(define (third x)

(common x 5)

)

(define (common n f)

(define (do-common x num)

(if (> (remainder x f) 0)

   num

    (do-common (/ x f) (+ num 1))

)

)

 (do-common n 0)

)