; useful code for CS 3 lab assignment 6

; Exercise 1

(define (mystery S so-far)
  (if (empty? S)
      so-far
      (mystery (bf S) (se (first S) so-far)) ) )


; Exercise 2

; Return the largest value in S, a nonempty sentence of numbers.
(define (sent-max1 S)
  (cond
    ( _____ )   ; base case
    ((> (first L) (first (bf L)))
     ( _____ ) )        ; recursive case
    (else
     ( _____ ) ) ) )    ; recursive case

; Return the largest value in S, a nonempty sentence
; of numbers.
(define (sent-max2 S)
  (sent-max-helper (bf S) _____ ) )

; Return the larger of max-so-far and the largest value
; in S, a (possibly empty) sentence of numbers.
(define (sent-max-helper S max-so-far)
  (if (empty? S) max-so-far
      (sent-max-helper (bf s) _____ ) ) )


; Exercise 3

(define (grouped roman-numeral)
  (cond
    ((empty? roman-numeral)  _____ )
    ((empty? (bf roman-numeral))  _____ )
    ((< _____  _____ )
     (se _____  _____ ) )
    (else 
     (se _____  _____ ) ) ) )

(grouped 'x)        ; should return (x)
(grouped 'xl)      ; should return (xl)
(grouped 'xli)    ; should return (xl i)
(grouped 'xliv)  ; should return (xl iv)
(grouped 'liv)    ; should return (l iv)
(grouped 'li)      ; should return (l i)