Question

I can’t seem to figure out how to write this function. What I am trying to write is a function expand that takes a list lst as a parameter of the form '(a (2 b) (3 c)) and is evaluated to '(a b b c c c)

Answer 1

This looks like homework, so I’m not giving you a straight answer. Instead, I’ll give you some pointers in the right direction. The most useful hint, is that you should split the problem in two procedures, one for processing the “outer” list and the other for generating the repetitions encoded in the inner sublists.

Notice that both procedures are mutually recursive (e.g., they call each other). The expand procedure recurs over the list, whereas the repeat procedure recurs over the number of repetitions. This is the general structure of the proposed solution, fill-in the blanks:

; input:  lst - list to be processed
; output: list in the format requested
(define (expand lst)
  (cond ((null? lst)             ; if the list is null
         '())                    ; then return null
        ((not (pair? (car lst))) ; if the first element of the list is an atom
         (cons <???> <???>))     ; cons the atom and advance the recursion
        (else                    ; if the first element of the list is a list
         <???>)))                ; call `repeat` with the right params


; input: n   - number of repetitions for the first element in the list
;        lst - list, its first element is of the form (number atom)
; output: n repetitions of the atom in the first element of lst
(define (repeat n lst)
  (if (zero? n)          ; if the number of repetitions is zero
      (expand (cdr lst)) ; continue with expand's recursion
      (cons <???>        ; else cons the atom in the first element and
            <???>)))     ; advance the recursion with one less repetition