; CSC151, Class 29: Deep Recrusion
; 
; Overview:
; * List Recursion, Revisited
; * Deep Recursion
; * Problem: count-elements
; * Problem: depth
; 
; Notes:
; * Reading for tomorrow: Higher-order procedures
; * Reese wrote notes for Friday's class.
; * Questions on vectors?
; * First result from conference: I'll work on guidelines 
;   for style.
; * Second result from conference: Temple Burling story.
; * Third result from conference: A "fun" exercise.
; * Sorry about the last homework.
; * Design of today's class

; Start with something we should know: Recursion over lists.
;  (1) Is the list null?
;  (2) If so, return base case
;  (3) Do something on the car and recurse on cdr.

; Sometimes we check if there's only one thing, rather than
; no things in the list.

; If we're adding all the elements and there's only one
; thing, use that thing.

; Repeated addition, subtraction, etc. may always need
; *two* elements.

; To check for only one element, use (null? (cdr lst))
; To check for no elements, use null?

; Find the length of a list
     
(define llength
  (lambda (lst)
    (if (null? lst)
        0
        (+ 1 (llength (cdr lst))))))

;;; Practica:
;;; > (count-values (list (list 1 2 3) 4 5 6 (list 7 8 9)))
;;; 9
;;; > (count-values (list 1 2))
(define count-values
  (lambda (lst)
    (cond
      ((null? lst) 0)
      ((list? (car lst)) 
       (+ (count-values (car lst)) (count-values (cdr lst))))
      (else
        (+ 1 (count-values (cdr lst)))))))