;;; File:
;;;   exam1.scm
;;; Author:
;;;   Samuel A. Rebelsky
;;;   The students of CSC153 2004S
;;; Summary:
;;;   Assorted notes on exam 3.

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Problem 1 ;
;;;;;;;;;;;;;

;;; Procedure:
;;;   number->digits
;;; Parameters:
;;;   num, a non-negative integer
;;; Purpose:
;;;   Compute the digits in num.
;;; Produces:
;;;   digits, a list of the form (d_k d_(k-1) ... d_3 d_2 d_1)
;;; Preconditions:
;;;   [See above]
;;; Postconditions:
;;;   "digits" is the digits of num in order.
;;;   d_i = (mod (quotient num (expt 10 (- i 1)) 10)
;;;   d_k is nonzero
;;;   Each of d_i is in the range [0..9]
(define digits->number
  (lambda (lst)
    (let kernel ((stuff (reverse lst))
                    (base 1))
      (if (null? stuff)
          0
          (+ (* base (car stuff)) (kernel (cdr stuff) (* base 10)))))))

(define number->digits
  (lambda (val)
    (map (lambda (x) (string->number (string x))) (string->list (number->string val)))))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Problem 2 ;
;;;;;;;;;;;;;

;;; Procedure:
;;;   alphabetically-first
;;; Parameters:
;;;   str1, str2, ... strk, 1 or more strings
;;; Purpose:
;;;   To find the parameter string that comes alphabetically
;;;     first.
;;; Produces:
;;;   smallest, a string
;;; Preconditions:
;;;   [standard]
;;; Postconditions:
;;;   (string-ci<=? smallest stri) for all reasonable i.

(define alphabetically-first
  (lambda lst
    (cond
      ((null? (cdr lst)) (car lst))
      ((null? (cddr lst)) 
       (if (string-ci<? (car lst) (cadr lst))
           (car lst)
           (cadr lst)))
      (else (alphabetically-first (car lst)
                                  (apply 
                                   alphabetically-first 
                                   (cdr lst)))))))

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Problem 3 ;
;;;;;;;;;;;;;

; > (value->string (list 'a 'b 'c))
; "(a b c)"
; > (value->string (list "a" "b" "c"))
; "(\"a\" \"b\" \"c\")"
; > (display (value->string (list "a" "b" "c")))
; ("a" "b" "c")
; > (value->string (list #\a #\b #\c))
; "(\#a \#b \#c)"

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; Problem 4 ;
;;;;;;;;;;;;;

;;; Procedure:
;;; lookup
;;; Parameters:
;;; name, a string
;;; collection, a list of three-element lists
;;; Purpose:
;;; Find all entries in the catalog with certain last name
;;; Produces:
;;; matches, a list of three-element lists representing all
;;; of the matching entries
;;; Preconditions:
;;; name is a string [unverified]
;;; collection is a valid list of three-element lists
;;; Postconditions:
;;; matches contains all elements of collection for which
;;; it is true that (string=? name (car element))
(define lookup
  (lambda (name collection)
    (letrec ((validcollection?
              (lambda (collection)
                (if (list? collection)                    
                    (if (null? (cdr collection))
                        (if (list? (car collection))
                            (if (= (length (car collection)) 3)
                                #t
                                #f)
                            #f)
                        (if (list? (car collection))
                            (if (= (length (car collection)) 3)
                                (validcollection? (cdr collection))
                                #f)
                            #f)))))
             (find
              (lambda (name collection)
                (if (null? collection)
                    null
                    (if (string=? name (car (car collection)))
                        (cons (car collection)
                              (find name (cdr collection)))
                        (find name (cdr collection)))))))
      (if (validcollection? collection)
          (find name collection)
          (error "Invalid collection")))))