; CS101, Spring 2013
; Lab 3

; Using decision statements to solve a problem.

(display "\n         CS101 Lab 3, Spring 2013\n")
(display "\n                SOLUTIONS\n\n")
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; READ THE DIRECTIONS FOR EACH PROBLEM CAREFULLY BEFORE STARTING TO WRITE
; YOUR SOLUTIONS.

(display "Problem 1: Twentieth-Century Postage Charges.\n\n")
; 
;  The Post Office charges the following postage for a first-class letter, 
;  depending upon its weight:
;       o less than 30 grams, 15 cents,
;       o 30 to 49 grams, 17 cents,
;       o 50 to 99 grams, 22 cents,
;       o 100 grams and over, 1 cent for each 4 grams. In this case,
;         round the value obtained by dividing grams by 4 to the nearest 
;         integer (use the function round).
;       
;  Write a procedure that consumes the weight in grams and returns the
;  postage in cents. Follow the design recipe, including contract, header,
;  purpose, pre-function tests, function definition, and post-function
;  printfs for results. Be sure you test every possible branch of execu-
;  tion.
;  
;  Note: This function will involve making decisions.  When more than 2
;  different conditions may occur, the best special form to use is a cond.
;  
;  Define seven constants in the global environment for the values 30, 
;  50, 100, 15, 17, 22, and 4.  Name these constants appropriately and 
;  use the names in your procedure definition.
;  
;  It may help you to write the function first using literal values in
;  the function body and then replace the literal values with the constant 
;  names after you know where the constant names should be placed in the 
;  function. Be sure to type the constant names in the function and in
;  the check-expect statements before you submit this lab.
;          


;Constant values used in procedure:
(define LOWER-CUTOFF 30)
(define LOWEST-RATE 15)
(define MID-CUTOFF 50)
(define MID-RATE 17)
(define MID->HIGH-CUTOFF 100)
(define MID->HIGH-RATE 22)
(define INCREMENT 4)

;Contract: (postage number) -> number
;Header:   (define postage (lambda (grams) ...))
;Purpose:  Calculate the postage charges as given in the above comment box.
;Pre-function tests:
(check-expect (postage 29) 15)
(check-expect (postage 30) 17)
(check-expect (postage 50) 22)
(check-expect (postage 100) 25)
(check-expect (postage 101) 25)
(check-expect (postage 102) 26)
(check-expect (postage 104) 26)
;Function definition:
(define postage
  (lambda (grams)
    (cond
      ; letter weighs less than 30 grams
      [(< grams LOWER-CUTOFF) LOWEST-RATE]
      ; letter weighs between 30 and 49 grams
      [(< grams MID-CUTOFF) MID-RATE]
      ; letter weighs between 50 and 99 grams
      [(< grams MID->HIGH-CUTOFF) MID->HIGH-RATE]
      ; letter weighs 100 grams or over
      [else (round (/ grams INCREMENT))])))


;Post-function printf's: (uncomment when ready)
(printf "(postage 29) => ~a~%" (postage 29))
(printf "(postage 30) => ~a~%" (postage 30))
(printf "(postage 50) => ~a~%" (postage 50))
(printf "(postage 100) => ~a~%" (postage 100))
(printf "(postage 104) => ~a~%" (postage 104))


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(display "Problem 2: A function to calculate speeding fines\n\n")
; 
;  The government has set new fines for speeding, as follows: 
;     - If the motorist was observed traveling over the speed limit:
;       * If the motorist's speed was less than 40% above the speed 
;         limit, the basic fine is $50.
;       * If the motorist was traveling 40% above the speed limit or 
;         more, the basic fine is $100.
;     - Otherwise, the fine is 0.   
;       
;  The actual fine is computed as the square of the number of speeding 
;  tickets the motorist has received in the last three years multiplied
;  by the basic fine for their speed.  Thus, a motorist traveling 70 km/hr 
;  in a 50 km/hr zone, with 3 prior speeding tickets in the last three 
;  years, will pay $100 * 3^2 = $900. (The hope is that motorists will
;  stop speeding or, if not, the government's financial problems will 
;  be solved forever!)
;  
;  Part I: Define 3 constants in the global environment- 
;          i) the lower basic fine ($50),
;         ii) the upper basic fine ($100), and
;        iii) the cut-off for percentage above the limit (0.40).  
;  
;  Part II: Define the function using the design recipe, including 
;           contract, header, purpose, pre-function tests, function
;           definition, and post-function printfs.
;  
;       The function should consume three inputs:
;       1) The speed of the motorist as detected by the highway 
;          patrol,
;       2) the speed limit for the zone the motorist was pulled
;          over in (in km/hr), and
;       3) the number of speeding tickets the motorist has 
;          received over the past three years.
; 
;  Be careful to make your function give the correct fine to those lucky
;  motorists who have received 0 speeding tickets in the last 3 years.
; 
;  It may help you to write the function first using literal values in
;  the function and to then replace the literal values with the constant 
;  names after you know where the constant names should be placed in the 
;  function. Be sure to type the constant names in the function and in
;  the check-expect statements before you submit this lab.
;  

 
;Constants representing the lower and upper basic fine amounts:
(define LOWER-FINE 50)
(define UPPER-FINE 100)
(define PERCENTAGE-OVER 0.4)

;Contract: (calc-fine number number number) -> number
;Header:   (define calc-fine 
;             (lambda (motorist-speed speed-limit num-tickets) ... ))
;Purpose:  To calculate the speeding fine for motorist exceeding the
;          speed limit based on clocked speed and number of past tickets.
;Pre-function tests:
(check-expect (calc-fine 70 50 3) 900)
(check-expect (calc-fine 75 55 2) 200)
(check-expect (calc-fine 95 55 0) 100)
(check-expect (calc-fine 95 55 1) 100)
(check-expect (calc-fine 95 55 3) 900)
(check-expect (calc-fine 76 55 0) 50)
(check-expect (calc-fine 76 55 2) 200)
(check-expect (calc-fine 55 55 2) 0)


;Function definition:
(define calc-fine
  (lambda (motorist-speed speed-limit num-tickets)
    ;; was motorist speeding?
    (if (> motorist-speed speed-limit)
        ;; if so, calculate fine based on amount over the speed limit the
        ;; motorist was traveling plus the square of the number of tickets
        ;; they received in the last 3 years.
        (if (< motorist-speed (+ speed-limit (* speed-limit PERCENTAGE-OVER)))
            (* LOWER-FINE (if (= num-tickets 0) 1 (sqr num-tickets)))
            (* UPPER-FINE (if (= num-tickets 0) 1 (sqr num-tickets))))
        ;; if the motorist was not speeding, fine is 0
        0)))

;Post-function tests:
(printf "(calc-fine 70 50 3) => $~a~%" (calc-fine 70 50 3))
(printf "(calc-fine 75 55 2) => $~a~%" (calc-fine 75 55 2))
(printf "(calc-fine 95 55 0) => $~a~%" (calc-fine 95 55 0))
(printf "(calc-fine 95 55 1) => $~a~%" (calc-fine 95 55 1))
(printf "(calc-fine 95 55 3) => $~a~%" (calc-fine 95 55 3))
(printf "(calc-fine 76 55 0) => $~a~%" (calc-fine 76 55 0))
(printf "(calc-fine 76 55 2) => $~a~%" (calc-fine 76 55 2))
(printf "(calc-fine 55 55 3) => $~a~%" (calc-fine 55 55 3))


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