; CS 60 Assignment 1         Functional Programming Warmup        100 points total
; 
; Author: Use_your_own_name
;
; ALWAYS put your own name after the header.
;
; Due Sunday 1/24/2010 at 11:59 p.m. at the web submission site:
;
;     http://www.cs.hmc.edu/~cs60grad/submissions/submit.py
;
; The first time you use Dr. Scheme, select the language "Pretty Big", which
; is what we will be using for the Scheme part of the course.
;
; Add your solution definitions to this file, load it as Scheme code,
; then submit it when you are happy with the results. You may submit multiple
; times. Only the last submission will be graded.
;
; Please first download to your directory the tester.scm file from the web page, 
; so that the unit tests make sense.
;
; Put it in the same directory from which you load your file, so that it will be
; loaded whenever you load your file. This tester is used for all Scheme-based
; assignments.
;
; NOte: There is a built-in test facility in Dr. Scheme, but please
; DO NOT use it, as it will convert all of your source code into XML,
; making it impossible for anyone to read as text.)

(load "tester.scm")

; When run as is, all tests will fail. By replacing the definitions
; with correct ones, you should get more tests succeeding, and eventually
; all tests should succeed.
;
; We provide at least one unit test for every function. You may wish to add
; some more tests of your own, to check yourself. You may leave your unit tests 
; in the submitted file. We will be using a different unit test facility and 
; will test your definitions on examples that you haven't seen.
;
; You do not have to worry about checking for malformed input. We will not be
; using any test cases such as that.
;
; You should pay attention to elegance, readability, and comments where needed.
; Formatting should be straightforward if you use Dr. Scheme, since it indents
; for you.
;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; All answers MUST be done using functional programming.                       ;
; Do not use assignment!                                                       ;
; Do not use conventional iteration. It isn't needed.                          ;
; The emphasis here is on constructing and composing functions. Non-compliant  ;
; solutions will be counted as wrong. If you don't know how to approach a      ;
; problem in the prescribed way, please seek help at your earliest opportunity.;
;                                                                              ; 
; Include comments and use meaningful identifiers where possible.              ; 
; Make your solutions elegant and clear as possible.                           ;
; We are interested in style, rather than simply answers.                      ;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

; Problem 1: [10 points]
;
; Heron's formula for the area of a triangle given its three sides is
; a beautiful little formula. You find its definition on the wikipedia
; http://en.wikipedia.org/wiki/Heron%27s_formula
;
; Devise a comparably beautiful Scheme function 'heron' with three arguments
; that computes the area based on this formula. Use a 'let' for the value
; of s so that you don't repeat sub-expressions. The built-in 'sqrt' can be
; used to extract the square root.

(define (heron a b c) 0) ;; Replace with the correct definition

; Unit tests for heron
(test (heron 3 4 5) 6)
(test (heron 12 13 5) 30)
(test (heron 42 29 29) 420)
(test (heron 1e10 1e10 1) 5e9)
(test (heron 1 1 1) (/ (sqrt 3) 4))


; Problem 2: [20 points]
;
; Look up Zeller's congruence in the wikipedia. This is a formula for finding the day
; of the week of any day in the Gregorian calendar (the calendar we usually use) given the
; year, month, and date. Give a scheme definition of function 'zeller', wherein the
; year, month, and day are numbers, as indicated on the web page, and the returned value
; is the number of the day of a week, starting with 0 for Saturday, 1 for Sunday, etc.
; Note that the translation of "January and February are counted as months 13 and 14 
; of the previous year" is a little tricky. In effect, the previous year must be used when
; these months arise. This can be handled by over-riding year using a 'let'.

(define (zeller year month day) 0) ;; Replace with the correct definition

(test (zeller 1975 7 20) 1)
(test (zeller 1991 5 1) 4)
(test (zeller 2000 1 11) 3)


; Problem 3:  [10 points]
;
; Define a function 'month-number that returns the number of a symbolic month, given the
; Scheme symbol for the month. The month symbols are to be 3-letter symbols, 'jan, 'feb, ...
; and the numbers run from 1 to 12. (Use the assoc built-in function.)

(define (month-number month-name) 12) ;; Replace with the correct definition

(test (month-number 'sep) 9)
(test (month-number 'jul) 7)
(test (month-number 'jan) 1)


; Problem 4: [10 points]
;
; Define a function 'day-name' that returns a 3-letter day symbol, given the number to
; which the day would correspond as the output of 'zeller'.

(define (day-name day-number) 'fri) ;; Replace with the correct definition

(test (day-name 3) 'tue)
(test (day-name 0) 'sat)
(test (day-name 1) 'sun)


; Problem 5: [10 points]
;
; Compose the functions in your previous definitions to give a more user-friendly
; version of 'zeller', which we call 'day-of-week'. This takes a year,
; a month symbol, and a day of the month and returns a day-of-the-week symbol.
; Maybe test it on your own birthday.

(define (day-of-week year month-name day) 'fri)  ;; Replace with the correct definition

(test (day-of-week 1975 'jul 20) 'sun)
(test (day-of-week 1979 'dec  2) 'sun)
(test (day-of-week 2000 'jan 11) 'tue)


; Problem 6: [5 points]
;
; Given below is an association list that gives a Scrabble letter score for
; each of the 26 letters of the alphabet. Use this association list to create a
; function 'score-letter' that will return the score of its argument letter.
; Have your function return 0 if the argument is not a letter.

(define scrabble-letter-scores
  '((#\a 1) (#\b 3) (#\c 3) (#\d 2) (#\e 1) (#\f 4) (#\g 2) 
    (#\h 4) (#\i 1) (#\j 8) (#\k 5) (#\l 1) (#\m 3) 
    (#\n 1) (#\o 1) (#\p 3) (#\q 10)(#\r 1) (#\s 1) (#\t 1)
    (#\u 1) (#\v 4) (#\w 4) (#\x 8) (#\y 4) (#\z 10) ))

(define (score-letter letter) -1)  ;; Replace with the correct definition

(test (score-letter '#\w)  4)
(test (score-letter '#\z) 10)
(test (score-letter '_)    0)


; Problem 7: [10 points]
;
; Construct a function score-word that scores an entire word represented as a symbol. 
; Use higher-order functions such as foldr and map to do any necessary iteration implicitly.
; Note that symbols are not the same as strings. However, the built-in function 
; symbol->string will convert a symbol into a  string of characters, and the built-in function 
; string->list will convert a string into a list of its characters.

(define (score-word word) 0)  ;; Replace with the correct definition

(test (score-word 'foo) 6)
(test (score-word 'aeiou) 5)
(test (score-word 'abcdefghijklmnopqrstuvwxyz) 87)
(test (score-word 'bcdfghjklmnpqrstvwxyz) 82)


; Problem 8: [25 points]
;
; Construct a function that finds the highest-scoring word in a list of symbols,
; returning both the word and the score as a list of two elements. This may require
; the invention of some helper functions. For the case that the list of symbols is empty,
; return the following dummy value: '(_ 0)

(define (highest-word-score list-of-words) '(foo 0))  ;; Replace with the correct definition

(test (highest-word-score '(two words)) '(words 9))
(test (highest-word-score '(one_word))  '(one_word 11))
(test (highest-word-score '(the quick brown fox just plays with my very lazy dog)) 
      '(quick 20))
(test (highest-word-score 
      '(now is the time for each good person to come to the aid of his or her party)) 
      '(party 10))
(test (highest-word-score '()) '(_ 0))


; Extra Credit Problem 9: [25 points extra] 
;
; Construct a function best-word that returns the highest Scrabble-scoring symbol  
; among the symbols in the second argument 
; that can be created by using each letter in the first argument at most once. 
; If there is a tie, an arbitrary one of the symbols in the list with maximal
; score can be returned. (In grading your problems, we will make sure that the chosen word 
; in each test case is unique.) Examples of successful unit tests are given after the stub definition.
 
; Notice that in the second example, two p’s of apple were used to form 'pape, while in the 
; third example, 'pape could not be made because of too few p’s in 'pale. Try to give 
; some attention to efficiency in your solution. For example, enumerating all permutations 
; of the letters in the first argument would not be a good idea, because perhaps relatively 
; few of those permutations occur in the second argument list. 

(define (best-word symbol list-of-words) '())

; Uncomment these if you do the exta credit problem:
;
;(test (best-word 'academy '(ace ade cad cay day)) '(cay 8)) 
; 
;(test (best-word 'apple   '(peal peel ape pape))  '(pape 8)) 
; 
;(test (best-word 'pale    '(peal peel ape pape))  '(peal 6)) 
; 

; The following will give the overall number of tests correct and incorrect:

(tester 'show)