Problem$^a$ 4.  Develop a program that counts the number of unknowns in a list of family trees:

(define-struct unknown (optional))
(define-struct parents (mom dad))

;; A LOFT is one of: 
;; -- empty 
;; -- (cons FT LOFT)

;; A FT is one of: 
;; -- (make-unknown String)
;; -- (make-parents FT FT)

Solution

(define tree1 (make-unknown 'a))
(define tree2 (make-parents (make-unknown 'b) (make-unknown 'c)))

(define forest1 empty)
(define forest2 (cons tree1 (cons tree2 empty)))

;; count-tree : FT -> Number [PT 1]
;; count the unknowns in a tree [PT 1]
(define (count-tree t) 
  (cond ;; [PT 1 for 2 correct cond lines/quest]
    [(unknown? t) 1] ;; [PT 1 for correct "recursions"]
    [else (+ (count-tree (parents-mom t)) (count-tree (parents-dad t)))]))

;; count-forest : LOFT -> Number [PT 1]
;; count the unknowns in a forest [PT 1]
(define (count-forest f) 
  (cond ;; [PT 1 for 2 correct cond lines/quest]
      [(empty? f) 0]
      ;; [PT 1 for correct "recursions"]
      [else (+ (count-tree (first f)) (count-forest (rest f)))]))

;; Examples/Tests: [PT 2, one each]
(= (count-tree tree2) 2)
(= (count-forest forest2) 3)