;;
;; Answers to CS3 2001 Summer Final Exam (by Lisa Nguyen)
;;

;; Question 1
;; Part a
;; (cons cons cons) ;; ==> (#[procedure cons] . #[procedure cons])

;; Part b
;;    _ _ _  _ _ _     _ _ _  _ _ _    _ _ _  _ _ _    _ _ _  _ _ _
;;   |      |     |  |      |      | |      |      | |      |    / |
;;-->|      |  - - ->|      |  - - ->|      |  - - ->|      |  /   |
;;   |_ | _ |_ _ _|  |_ | _ |_ _ _ | |_ | _ |_ _ _ | |_ | _ |/ _ _ |
;;      |               |               |               |
;;      |               \/              \/              \/
;;      \/               3              4               5
;;    _ _ _  _ _ _    _ _ _  _ _ _   
;;   |      |      | |      |    / |
;;   |      |  - - ->|      |  /   |
;;   |_ | _ |_ _ _ | |_ | _ |/ _ _ |
;;      |               | 
;;      \/              \/ 
;;       1               2

;; Part c
;; Name: SHOW-ME-THE-TRUTH
;; Inputs: A single argument of any data type, bool
;; Requires: None
;; Side Effects: Displays "false" and newline if bool is #f, and
;;               displays "true" and a newline otherwise.
;; Returns: #f
;; Examples: (show-me-the-truth #t) ==> #f
;;                                  ==P [true
;; ]

;; Part d
;;          a
;;         / \
;;        b   c
;;            /\
;;           d  e

;; Part e
;; MYSTERY will return an error if given a tree with only one child.

;; Part f
;; Q: If I type (mystery thistree), what return value do I get?
;; A: this-is-hard
;; Q: Write all of the side effects of (mystery thistree)?
;; A: b
;;    d
;;    e
;;    c
;;    a

;; Question 2
;; Part a we're skipping because we didn't read this chapter this year.

;; Part b
;; month-name, date-in-month

;; Part c
;; ABSTRACTION - You only needed to change two functions in datesv1.scm because
;; you use selectors.  Because the rest of the code uses the selectors, it
;; doesn't really matter how the dates are actually implemented.  If we hadn't
;; used selectors in the rest of the code, and just assumed that the month 
;; would be car and the date would be cadr, you would have to change ALL the 
;; functions in datesv1.scm.

;; Question 3
(define (cooler-deeper-count ltr s)
    (accumulate 
      + 
      (every 
        (lambda (wd) 
          (count (keep (lambda (l) (equal? ltr l)) wd))) 
        s)))

;; Question 4
(define (make-term coeff expt)
  (cond 
    ((= coeff 0) 0)
    ((= expt 0) coeff)
    ((and (= coeff 1) (= expt 1)) 'x)
    ((= coeff 1) (word 'x^ expt))
    ((= expt 1) (word coeff 'x))
    (else (word coeff 'x^ expt))))

;; requires wd be in s
;; counts from 0
(define (position wd s)
  (if (equal? wd (first s))
      0
      (+ 1 (position wd (bf s)))))

(define (get-coefficient exp)
  (cond
    ((equal? (first exp) 'x) 1)
    ((not (member? 'x exp)) exp)
    (else ((repeated bl (- (count exp) (position 'x exp))) exp))))

(define (get-exponent exp)
  (cond 
    ((number? exp) 0)
    ((not (member? '^ exp)) 1)
    (else ((repeated bf (+ 1 (position '^ exp))) exp))))

(define (deriv-term exp)
  (make-term (* (get-coefficient exp)
                (get-exponent exp))
             (- (get-exponent exp) 1)))