#lang racket

; CS 60 Assignment 1         Functional Programming Warmup        100 points total
; 
; Author: Always_replace_this_with_your_own_name
;
; ALWAYS: put your own name after the header.
;
; Due Wed. 8 September 2010 at 11:59 p.m. at the web submission site:
;
;     http://www.cs.hmc.edu/~submissions/submissions

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
; ABSOLUTE REQUIREMENT:                                                        ;
;                                                                              ;
; All answers MUST be use pure 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.                      ;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(require htdp/testing) ; Incant to get check-expect, check-within, generate-report

; IMPORTANT:
;
; The first time you use Dr. Racket, go to the menu bar, select Language, 
; then select "Use the language declared in the source."
;
; Add your solution definitions to this file, by replacing the placeholder
; definitions, such as 0, with your own expressions.
; Submit the whole file when you are happy with the results. 
; You may submit multiple times. Only the last submission will be graded.
;
; When run as is, all tests will fail. By replacing the definitions
; with correct ones, you should gradually get more tests to succeed.
; 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 testing your definitions on examples that you haven't seen, so
; the more testing you do to enhance your confidence in the solutions, the better.
;
; 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. Racket, since it indents
; for you.
; DO NOT, under any circumstances, present a large definition on just a single line.
; We hate this, and will ream your score for doing it.
; Ideally our lines are at most 80 characters long, but some of these go to 90 or so.
; Try not to use more than that. Your code should be viewable on a standard
; 8.5 x 11 sheet in portrait mode, without any line wrapping.


; Problem 1: [10 points]
;
; Heron's elformula 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 Racket 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
(check-expect (heron 3 4 5) 6)
(check-expect (heron 12 13 5) 30)
(check-expect (heron 42 29 29) 420)
(check-within (heron 1e10 1e10 1) 5e9 1)
(check-within (heron 1 1 1) (/ (sqrt 3) 4) 1e-16)

; Note that we use check-expect when answers can be compared exactly (e.g. integers).
; When floating point (i.e. scientific notation, such as 1e10) is involved, Racket
; will not let you use check-expect. Instead, use check-within, which has a third
; argument, the tolerance allowed for the answer.
; Use a 'let to avoid recomputation.


; 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 Racket 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'.
; Note that 'quotient is the integer division function, and 'modulo is remainder.
; Note: This is an exercise in using 'let, so use use it.

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

; Unit tests for zeller
(check-expect (zeller 1975 7 20) 1)
(check-expect (zeller 1991 5 1) 4)
(check-expect (zeller 2000 1 11) 3)


; Problem 3:  [10 points]
;
; Use the builtin function 'assoc to define a function 
; 'month-number that returns the number of a symbolic month, given the
; Racket symbol for the month. The month symbols are to be 3-letter symbols, 
; 'jan, 'feb, ...
; and the numbers run from 1 to 12.
; Note: This is an exercise in assoc. If you don't use it, you lose points.


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

; Unit tests for month-number
(check-expect (month-number 'sep) 9)
(check-expect (month-number 'jul) 7)
(check-expect (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'.
; Note: You might think we want to use assoc here. No. Try using list-ref instead.

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

; Unit tests for day-name
(check-expect (day-name 3) 'tue)
(check-expect (day-name 0) 'sat)
(check-expect (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

; Unit tests for day-of-week
(check-expect (day-of-week 1975 'jul 20) 'sun)
(check-expect (day-of-week 1979 'dec  2) 'sun)
(check-expect (day-of-week 2000 'jan 11) 'tue)
(check-expect (day-of-week 1944 'jun 12) 'mon)


; 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

; Unit tests for score-letter
(check-expect (score-letter '#\w)  4)
(check-expect (score-letter '#\z) 10)
(check-expect (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.
; Consider creating symbol->list which is the composition of those two functions.
; It might be handy.

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

; Unit tests for score-word
(check-expect (score-word 'foo) 6)
(check-expect (score-word 'aeiou) 5)
(check-expect (score-word 'abcdefghijklmnopqrstuvwxyz) 87)
(check-expect (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

; Unit tests for highest-word-score
(check-expect (highest-word-score '(two words)) '(words 9))
(check-expect (highest-word-score '(one_word))  '(one_word 11))
(check-expect (highest-word-score '(the quick brown fox just plays with my very lazy dog)) 
      '(quick 20))
(check-expect (highest-word-score 
      '(now is the time for each good person to come to the aid of his or her party)) 
      '(party 10))
(check-expect (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. 
;
; Hint: You might make use of a recursively-defined helper function for this one.

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

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

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

(generate-report)