;; CIS 352, EXAM 1: Distributions of Scores

;; Range    Scores
;; 21- 30:  30
;; 31- 40:  37
;; 41- 50:  44 49
;; 51- 60:  51 53 54 54 57
;; 61- 70:  67 69
;; 71- 80:  74 74 75 75 76 80
;; 81- 90:  81 83 85 85 87
;; 91-100:  92
;;
;; Average: 66.61      Median: 74.0

(define displayln 
  (lambda items
    (map (lambda (x) (display x) (display " ")) items)
    (newline)))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Question 1.
(define a 0) 
(define b 3) 
(define c 6) 

(define one '((1 2) (3 4) (5 6))) 
(define two '(a b c)) 
(define three '(100 200 300)) 
(define four (cons 'two three)) 
(define result (let ((a 1) 
                     (b (* a 10)) 
                     (c (+ b a))) 
                 (let ((c 0) 
                       (b (+ c 1))) 
                   (list a b c)))) 
(define sample 
  (lambda x (cons a (length x)))) 

(displayln "**Question 1**")

(displayln "Question 1a: (cdar one) ~~>                    " (cdar one))

(displayln "Question 1b: four ~~>                          " four)

(displayln "Question 1c: (equal? (cons a b) '(a . b) ) ~~> "  (equal? (cons a b) '(a . b) ))

(displayln "Question 1d: (append three one) ~~>            " (append three one))

(displayln "Question 1e: (map cdr one) ~~>                 " (map cdr one))

(displayln "Question 1f: (map cons two three) ~~>          "  (map cons two three))

(displayln "Question 1g: result ~~>                        " result)

(displayln "Question 1h: (sample '((z y) w y)) ~~>         "  (sample '((z y) w y)))

(displayln "Question 1i: (apply sample one) ~~>            " (apply sample one))


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Question 2.

;; a. list, because it takes an arbitrary number of arguments

;; b.  +---+---+   +---+---+   +---+---+   +---+---+   +---+---+   
;;     | 1 | ----->| 2 | ----->| 3 | ----->| 4 | ----->| 5 | / |
;;     +---+---+   +---+---+   +---+---+   +---+---+   +---+---+   
;; 
;; c.  +---+---+   +---+---+               +---+---+
;;     | 1 | ----->| | | ----------------->| | | / |
;;     +---+---+   +-|-+---+               +-|-+---+
;;                   |                       | 
;;                   V                       V
;;                 +---+---+   +---+---+   +---+---+   +---+---+   
;;                 | 2 | ----->| 3 | / |   | 4 | ----->| 5 | / |
;;                 +---+---+   +---+---+   +---+---+   +---+---+   
;; 
;; d.  +---+---+               +---+---+   +---+---+
;;     | | | ----------------->| 3 | ----->| | | / |
;;     +-|-+---+               +-|-+---+   +-|-+---+
;;       |                                   | 
;;       V                                   V
;;     +---+---+   +---+---+   +---+---+   +---+---+   
;;     | 1 | ----->| / | ----->| 2 | 4/|   | 4 | 5 |
;;     +---+---+   +---+---+   +---+---+   +---+---+   


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(displayln "\n\n**Question 3**")

(define diag 
  (lambda (proc)
    (lambda (x) (proc x x))))

(define my-proc (diag cons))

(displayln "(my-proc 'a) ~~> " (my-proc 'a))
(displayln "(my-proc 10) ~~> " (my-proc 10))
(displayln "((diag +) 1) ~~> " ((diag +) 1))
(displayln "((diag *) 7) ~~> " ((diag *) 7))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(displayln "\n\n**Question 4**")

(define longest
  (lambda xss
    (if (null? xss) 
        0 
        (max (length (car xss)) (apply longest (cdr xss))))))

(define longest-also
  (lambda xss
    (if (null? xss)
        0        
        (apply max (map length xss)))))


(displayln "(longest '(1 2 3) '(a b c d e) '() '(#t #f))       ~~> " 
           (longest '(1 2 3) '(a b c d e) '() '(#t #f)))
(displayln "(longest)                                          ~~> " 
           (longest))

(displayln "(longest-also '(1 2 3) '(a b c d e) '() '(#t #f))  ~~> " 
           (longest-also '(1 2 3) '(a b c d e) '() '(#t #f)))
(displayln "(longest-also)                                     ~~> " 
           (longest-also))




;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(displayln "\n\n**Question 5**")
(define zip
  (lambda (lst1 lst2)
    (if (or (null? lst1) (null? lst2))
        ()
        (cons (cons (car lst1) (car lst2))
              (zip (cdr lst1) (cdr lst2))))))

(displayln "(zip '(a b c d e) '(1 2 3))         ~~~> "
            (zip '(a b c d e) '(1 2 3)))
(displayln "(zip '(a b c d e) '(1 2 3 4 5 6 7)) ~~~> "
           (zip '(a b c d e) '(1 2 3 4 5 6 7)))
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
(displayln "\n\n**Question 6**")

(define remove-all
  (lambda (sym slst)
    (cond 
      ((null? slst) ())
      ((symbol? (car slst))
       (if (eqv? sym (car slst))  
           (remove-all sym (cdr slst))
           (cons (car slst) (remove-all sym (cdr slst)))) )
      (else (cons (remove-all sym (car slst)) (remove-all sym (cdr slst)))))))

(define remove-all-too
  (lambda (sym slst)
    (apply append (map (lambda (se) (rm-all-se sym se)) slst))))

(define rm-all-se
  (lambda (sym se)
    (if (symbol? se)
        (if (eqv? se sym) () (list se))
        (list (remove-all-too sym se)))))

(displayln "(remove-all 'a '(a b a c d))              ~~~> " (remove-all 'a '(a b a c d)))
(displayln "(remove-all 'e '(a b a c d))              ~~~> " (remove-all 'e '(a b a c d)))
(displayln "(remove-all 'a '(a (b a c) () d (e)))     ~~~> " 
           (remove-all 'a '(a (b a c) () d (e))))

(displayln "(remove-all-too 'a '(a b a c d))          ~~~> " 
           (remove-all-too 'a '(a b a c d)))
(displayln "(remove-all-too 'e '(a b a c d))          ~~~> " 
           (remove-all-too 'e '(a b a c d)))
(displayln "(remove-all-too 'a '(a (b a c) () d (e))) ~~~> " 
           (remove-all-too 'a '(a (b a c) () d (e))))