#lang racket
(require htdp/testing)

;; this file:  hw3pr2.rkt
;; name(s):



; Test!
; - Use the check-expect tests provided
; - Add one of your own for each function:



; problem 1
(define (gcd a b)
  42)







; problem 2
(define (most-multiples L)
  42)










;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; The unit-calculator application - in Racket
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;-------------------------------------------------------
;; Provided functions - for comparing and sorting symbols
;;
;; comparing symbols alphabetically requires conv. to strings
(define (sym<? sym1 sym2)
  (string<? (symbol->string sym1) (symbol->string sym2)))

;; a function for sorting lists of symbols: sortsym
(define (sortsym L) (sort L sym<?))

;; here's how to use sortsym (no third argument needed!)
(check-expect (sortsym '(b c a)) '(a b c))

;;--------------------------------------------------------

;; An "information structure" abstraction for quantity lists
;;
; Function: make-QL
; Input:
;    quant - a number
;    num - a list of symbols representing the units in the numerator
;    den - a list of symbols representing the units in the denominator
;    unc - a number: the absolute 1-sigma uncertainty associated with quant
; Output:
;    a representation of a quantity list
(define (make-QL quant num den unc)
  (list quant (sortsym num) (sortsym den) unc))         

; Accessor functions for our Quantity list abstraction
(define get-quant first)
(define get-num second)
(define get-den third)
(define get-unc fourth)

;;--------------------------------------------------------

;; A predicate for checking if two quantity lists are "equal"
;; We will need this for our check-expect tests
;;
;; equal-QLs: a predicate to check if two quantity lists
;;   are close enough to be considered the same, for testing
;;   We use 42/100000 as our threshold, naturally... .
(define (equal-QLs? QL1 QL2)
  (let* ((q1 (get-quant QL1))  (q2 (get-quant QL2))
         (N1 (get-num QL1))    (N2 (get-num QL2))
         (D1 (get-den QL1))    (D2 (get-den QL2))
         (u1 (get-unc QL1))    (u2 (get-unc QL2)))
    (and ;; and can take any number of arguments!
     (< (abs (- q1 q2)) 4.2e-3)
     (< (abs (- u1 u2)) 4.2e-3)
     (equal? N1 N2)
     (equal? D1 D2))))

(check-expect (equal-QLs? (make-QL 42.0 '(m) '(s) 0.0)
                          (make-QL 42.0 '(m) '(s) 0.0))
              #t)


;;--------------------------------------------------------
;; Add your unicalc functions here...
;; Empty versions are available below:

(define (merge L1 L2)
  42) ;; not defined yet


(define (n-merge L n)
  42) ;; not defined yet


(define (cancel L1 L2)
  42) ;; not defined yet


(define (simplify QL)
  42) ;; not defined yet


(define (multiply QL1 QL2)
  42) ;; not defined yet


(define (power QL p)
  42) ;; not defined yet


(define (divide QL1 QL2)
  42) ;; not defined yet



;; norm-unit: normalizes a single unit - provided
;;  in:  a unit
;;  out: a NORMALIZED quantity list equivalent to that unit
;;  key: mutual recursion with norm-QL
;;
;;  Note: this is the ONLY unicalc function that needs UDB, the
;;        database of units defined at the very bottom of this file...
;;
(define (norm-unit unit)
  (if (not (assoc unit UDB))
      (make-QL 1.0 (list unit) '() 0.0)
      (norm-QL (second (assoc unit UDB)))))



(define (norm-QL QL)
  42) ;; not defined yet


(define (add QL1 QL2)
  42) ;; not defined yet


(define (subtract QL1 QL2)
  42) ;; not defined yet


;; the final conversion function (commented, for now):
;;
;(define (convert from to)
;  (norm-QL (divide from to)))

  

;;--------------------------------------------------------


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;; Define database for Unicalc
;; by Robert Keller
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(define unicalc-db-tiny 
  (list 
   (list 'day    (make-QL 24.0 '(hour)   '() 0.0))
   (list 'hour   (make-QL 60.0 '(minute) '() 0.0))
   (list 'minute (make-QL 60.0 '(second) '() 0.0))
   ))

(define unicalc-db-huge
  (list 
(list 'A                      (make-QL 1.0 '(ampere) '() 0.0))
(list 'amp                    (make-QL 1.0 '(ampere) '() 0.0))
(list 'amu                    (make-QL 1.0 '(atomic_mass_unit) '() 0.0))
(list 'atomic_mass_unit       (make-QL 1.0 '(dalton) '() 0.0))
(list 'AU                     (make-QL 1.0 '(astronomical_unit) '() 0.0))
(list 'bbl                    (make-QL 1.0 '(barrel) '() 0.0))
(list 'C                      (make-QL 1.0 '(coulomb) '() 0.0))
(list 'c                      (make-QL 1.0 '(speed_of_light) '() 0.0))
(list 'cal                    (make-QL 1.0 '(calorie) '() 0.0))
(list 'cd                     (make-QL 1.0 '(candela) '() 0.0))
(list 'cm                     (make-QL 1.0 '(centimeter) '() 0.0))
(list 'ev                     (make-QL 1.0 '(electron_volt) '() 0.0))
(list 'feet                   (make-QL 1.0 '(foot) '() 0.0))
(list 'fl_oz                  (make-QL 1.0 '(fluid_ounce) '() 0.0))
(list 'ft                     (make-QL 1.0 '(foot) '() 0.0))
(list 'F                      (make-QL 1.0 '(farad) '() 0.0))
(list 'gev                    (make-QL 1.0e9 '(ev) '() 0.0))
(list 'g                      (make-QL 1.0 '(gram) '() 0.0))
(list 'G                      (make-QL 1.0 '(gravitational_constant) '() 0.0))
(list 'h                      (make-QL 1.0 '(Planck_constant) '() 0.0))
(list 'hp                     (make-QL 1.0 '(horsepower) '() 0.0))
(list 'hr                     (make-QL 1.0 '(hour) '() 0.0))
(list 'H                      (make-QL 1.0 '(henry) '() 0.0))
(list 'Hz                     (make-QL 1.0 '(hertz) '() 0.0))
(list 'hertz                  (make-QL 1.0 '() '(second) 0.0))
(list 'in                     (make-QL 1.0 '(inch) '() 0.0))
(list 'inches                 (make-QL 1.0 '(inch) '() 0.0))
(list 'J                      (make-QL 1.0 '(joule) '() 0.0))
(list 'kilogram               (make-QL 1.0 '(kg) '() 0.0))
(list 'kilometer              (make-QL 1000.0 '(meter) '() 0.0))
(list 'km                     (make-QL 1.0 '(kilometer) '() 0.0))
(list 'kph                    (make-QL 1.0 '(kilometer) '(hour) 0.0))
(list 'kwh                    (make-QL 1.0 '(hour kilowatt) '() 0.0))
(list 'l                      (make-QL 1.0 '(liter) '() 0.0))
(list 'lb                     (make-QL 1.0 '(pound) '() 0.0))
(list 'litre                  (make-QL 1.0 '(liter) '() 0.0))
(list 'lm                     (make-QL 1.0 '(lumen) '() 0.0))
(list 'lx                     (make-QL 1.0 '(lux) '() 0.0))
(list 'm                      (make-QL 1.0 '(meter) '() 0.0))
(list 'megohm                 (make-QL 1000000.0 '(ohm) '() 0.0))
(list 'metre                  (make-QL 1.0 '(meter) '() 0.0))
(list 'mev                    (make-QL 1000000.0 '(electron_volt) '() 0.0))
(list 'mho                    (make-QL 1.0 '(siemens) '() 0.0))
(list 'microhm                (make-QL 1.0e-6 '(ohm) '() 0.0))
(list 'millimeter             (make-QL (/ 1.0 1000000) '(meter) '() 0.0))
(list 'millisecond            (make-QL (/ 1.0 1000000) '(second) '() 0.0))
(list 'min                    (make-QL 1.0 '(minute) '() 0.0))
(list 'mol                    (make-QL 1.0 '(mole) '() 0.0))
(list 'mm                     (make-QL 1.0 '(millimeter) '() 0.0))
(list 'mph                    (make-QL 1.0 '(mile) '(hour) 0.0))
(list 'ms                     (make-QL 1.0 '(millisecond) '() 0.0))
(list 'N                      (make-QL 1.0 '(newton) '() 0.0))
(list 'qt                     (make-QL 1.0 '(quart) '() 0.0))
(list 'pc                     (make-QL 1.0 '(parsec) '() 0.0))
(list 'pi                     (make-QL 3.14159265358979323846 '() '() 0.0))
(list 'psi                    (make-QL 1.0 '(pound_force) '(inch inch) 0.0))
(list 'pt                     (make-QL 1.0 '(pint) '() 0.0))
(list 'rpm                    (make-QL 1.0 '(revolution) '(second) 0.0))
(list 'S                      (make-QL 1.0 '(siemens) '() 0.0))
(list 's                      (make-QL 1.0 '(second) '() 0.0))
(list 'sec                    (make-QL 1.0 '(second) '() 0.0))
(list 'tbsp                   (make-QL 1.0 '(tablespoon) '() 0.0))
(list 'tsp                    (make-QL 1.0 '(teaspoon) '() 0.0))
(list 'T                      (make-QL 1.0 '(tesla) '() 0.0))
(list 'us                     (make-QL 1.0 '(microsecond) '() 0.0))
(list 'V                      (make-QL 1.0 '(volt) '() 0.0))
(list 'W                      (make-QL 1.0 '(watt) '() 0.0))
(list 'Wb                     (make-QL 1.0 '(weber) '() 0.0))
(list 'yd                     (make-QL 1.0 '(yard) '() 0.0))
(list 'yr                     (make-QL 1.0 '(year) '() 0.0))
(list 'acre                   (make-QL 43560.0 '(foot foot) '() 0.0))
(list 'apoth_dram             (make-QL 60.0 '(grain) '() 0.0))
(list 'apoth_ounce            (make-QL 480.0 '(grain) '() 0.0))
(list 'apoth_pound            (make-QL 5760.0 '(grain) '() 0.0))
(list 'are                    (make-QL 100.0 '(meter meter) '() 0.0))
(list 'angstrom               (make-QL 0.0000000001 '(meter) '() 0.0))
(list 'astronomical_unit      (make-QL 149600000000.0 '(meter) '() 0.0))
(list 'atmosphere             (make-QL 1013250.0 '(pascal) '() 0.0))
(list 'bar                    (make-QL 100000.0 '(pascal) '() 0.0))
(list 'barn                   (make-QL 1.0e-28 '(meter meter) '() 0.0))
(list 'barrel                 (make-QL 31.5 '(gallon) '() 0.0))
(list 'baryl                  (make-QL 1.0 '(dyne) '(centimeter centimeter) 0.0))
(list 'baud                   (make-QL 1.0 '(bit) '(second) 0.0))
(list 'bolt                   (make-QL 40.0 '(yard) '() 0.0))
(list 'british_gallon         (make-QL 1.20095 '(gallon) '() 0.0))
(list 'btu                    (make-QL 1055.06 '(joule) '() 0.0))
(list 'bucket                 (make-QL 18180.0 '(centimeter centimeter centimeter) '() 0.0))
(list 'bushel                 (make-QL 4.0 '(peck) '() 0.0))
(list 'byte                   (make-QL 8.0 '(bit) '() 0.0))
(list 'cable                  (make-QL 720.0 '(foot) '() 0.0))
(list 'carat                  (make-QL 200.0 '(milligram) '() 0.0))
(list 'caliber                (make-QL 0.001 '(inch) '() 0.0))
(list 'calorie                (make-QL 4.1868 '(joule) '() 0.0))
(list 'candle                 (make-QL 1.0 '(candela) '() 0.0))
(list 'centare                (make-QL 0.01 '(are) '() 0.0))
(list 'centimeter             (make-QL 0.01 '(meter) '() 0.0))
(list 'century                (make-QL 10.0 '(decade) '() 0.0))
(list 'chain                  (make-QL 66.0 '(foot) '() 0.0))
(list 'chronon                (make-QL 1.0e-24 '(second) '() 0.0))
(list 'coulomb                (make-QL 1.0 '(ampere second) '() 0.0))
(list 'cup                    (make-QL 0.5 '(pint) '() 0.0))
(list 'curie                  (make-QL 3.7037e10 '(becquerel) '() 0.0))
(list 'dalton                 (make-QL 1.6605654e-24 '(gram) '() 0.0))
(list 'daraf                  (make-QL 1.0 '() '(farad) 0.0))
(list 'day                    (make-QL 24.0 '(hour) '() 0.0))
(list 'decade                 (make-QL 10.0 '(year) '() 0.0))
(list 'degree                 (make-QL 1.0 '(radian) '(pi) 0.0))
(list 'dozen                  (make-QL 12.0 '() '() 0.0))
(list 'dram                   (make-QL 0.00390625 '(pound) '() 0.0))
(list 'dry_barrel             (make-QL 105.0 '(dry_quart) '() 0.0))
(list 'dry_pint               (make-QL 0.5 '(dry_quart) '() 0.0))
(list 'dry_quart              (make-QL 67.2 '(inch inch inch) '() 0.0))
(list 'dyne                   (make-QL 0.00001 '(newton) '() 0.0))
(list 'electron_volt          (make-QL 1.60218925e-20 '(joule) '() 0.0))
(list 'ell                    (make-QL 45.0 '(inch) '() 0.0))
(list 'em                     (make-QL 0.167 '(inch) '() 0.0))
(list 'en                     (make-QL 0.5 '(em) '() 0.0))
(list 'erg                    (make-QL 0.000001 '(joule) '() 0.0))
(list 'faraday                (make-QL 96490.0 '(coulomb) '() 0.0))
(list 'farad                  (make-QL 1.0 '(coulomb) '(volt) 0.0))
(list 'fathom                 (make-QL 6.0 '(foot) '() 0.0))
(list 'fermi                  (make-QL 1.0e-15 '(meter) '() 0.0))
(list 'fluid_dram             (make-QL 0.125 '(fluid_ounce) '() 0.0))
(list 'fluid_ounce            (make-QL 0.125 '(cup) '() 0.0))
(list 'flux_unit              (make-QL 1.0e-26 '(second watt) '(meter meter) 0.0))
(list 'foot                   (make-QL 12.0 '(inch) '() 0.0))
(list 'fortnight              (make-QL 2.0 '(week) '() 0.0))
(list 'free_acceleration      (make-QL 9.80665 '(meter) '(second second) 0.0))
(list 'furlong                (make-QL 40.0 '(rod) '() 0.0))
(list 'gallon                 (make-QL 231.0 '(inch inch inch) '() 0.0))
(list 'gauss                  (make-QL 0.0001 '(tesla) '() 0.0))
(list 'gilbert                (make-QL 1.0 '(ampere turn) '() 0.0))
(list 'gill                   (make-QL 0.25 '(pint) '() 0.0))
(list 'grain                  (make-QL 0.000142857 '(pound) '() 0.0))
(list 'gram                   (make-QL 0.001 '(kg) '() 0.0))
(list 'grav                   (make-QL 1.0 '(free_acceleration) '() 0.0))
(list 'gravitational_constant (make-QL 6.67259e-11 '(meter meter newton) '(kg kg) 0.0))
(list 'gross                  (make-QL 12.0 '(dozen) '() 0.0))
(list 'hectare                (make-QL 100.0 '(acre) '() 0.0))
(list 'henry                  (make-QL 1.0 '() '(ampere) 0.0))
(list 'hand                   (make-QL 4.0 '(inch) '() 0.0))
(list 'hogshead               (make-QL 63.0 '(gallon) '() 0.0))
(list 'horsepower             (make-QL 550.0 '(foot pound_force) '(second) 0.0))
(list 'hour                   (make-QL 60.0 '(minute) '() 0.0))
(list 'inch                   (make-QL 0.02539954113 '(meter) '() 0.0))
(list 'joule                  (make-QL 1.0 '(kg meter meter) '(second second) 0.0))
(list 'kilogram_force         (make-QL 1.0 '(free_acceleration kg) '() 0.0))
(list 'knot                   (make-QL 1.0 '(nautical_mile) '(hour) 0.0))
(list 'lambert                (make-QL 3.142 '(candela) '(centimeter centimeter) 0.0))
(list 'league                 (make-QL 3.0 '(mile) '() 0.0))
(list 'light_year             (make-QL 9406910000000000.0 '(meter) '() 0.0))
(list 'link                   (make-QL 7.92 '(inch) '() 0.0))
(list 'liter                  (make-QL 1000.0 '(centimeter centimeter centimeter) '() 0.0))
(list 'long_ton               (make-QL 2240.0 '(pound) '() 0.0))
(list 'lumen                  (make-QL 1.0 '(candela steradian) '() 0.0))
(list 'lux                    (make-QL 1.0 '(lumen) '(meter meter) 0.0))
(list 'maxwell                (make-QL 0.00000001 '(weber) '() 0.0))
(list 'metric_ton             (make-QL 1000.0 '(kg) '() 0.0))
(list 'micron                 (make-QL 0.000001 '(meter) '() 0.0))
(list 'mil                    (make-QL 0.001 '(inch) '() 0.0))
(list 'mile                   (make-QL 8.0 '(furlong) '() 0.0))
(list 'millenium              (make-QL 10.0 '(century) '() 0.0))
(list 'minute                 (make-QL 60.0 '(second) '() 0.0))
(list 'mole                   (make-QL 6.02253e23 '() '() 0.0))
(list 'nautical_mile          (make-QL 1.15078 '(mile) '() 0.0))
(list 'newton                 (make-QL 1.0 '(joule) '(meter) 0.0))
(list 'ohm                    (make-QL 1.0 '(volt) '(ampere) 0.0))
(list 'oil_barrel             (make-QL 42.0 '(gallon) '() 0.0))
(list 'ounce                  (make-QL 0.0625 '(pound) '() 0.0))
(list 'parsec                 (make-QL 30856770000000000 '(meter) '() 0.0))
(list 'pascal                 (make-QL 1.0 '(newton) '(meter meter) 0.0))
(list 'Planck_constant        (make-QL 6.626076e-34 '(joule second) '() 0.0))
(list 'peck                   (make-QL 8.0 '(dry_quart) '() 0.0))
(list 'pennyweight            (make-QL 24.0 '(grain) '() 0.0))
(list 'pica                   (make-QL 12.0 '(point) '() 0.0))
(list 'pint                   (make-QL 0.5 '(quart) '() 0.0))
(list 'point                  (make-QL 0.013837 '(inch) '() 0.0))
(list 'poise                  (make-QL 0.1 '(pascal) '(second) 0.0))
(list 'pound                  (make-QL 0.45359237 '(kg) '() 0.0))
(list 'pound_force            (make-QL 1.0 '(free_acceleration pound) '() 0.0))
(list 'poundal                (make-QL 1.0 '(foot pound) '(second second) 0.0))
(list 'quadrant               (make-QL 90.0 '(degree) '() 0.0))
(list 'quart                  (make-QL 0.25 '(gallon) '() 0.0))
(list 'revolution             (make-QL 4.0 '(quadrant) '() 0.0))
(list 'reyn                   (make-QL 68947.6 '(poise) '() 0.0))
(list 'rod                    (make-QL 16.5 '(foot) '() 0.0))
(list 'rood                   (make-QL 0.25 '(acre) '() 0.0))
(list 'rope                   (make-QL 20.0 '(foot) '() 0.0))
(list 'scruple                (make-QL 20.0 '(grain) '() 0.0))
(list 'section                (make-QL 1.0 '(mile mile) '() 0.0))
(list 'siemens                (make-QL 1.0 '(ampere) '(volt) 0.0))
(list 'skein                  (make-QL 360.0 '(foot) '() 0.0))
(list 'slug                   (make-QL 32.1740 '(pound) '() 0.0))
(list 'span                   (make-QL 9.0 '(inch) '() 0.0))
(list 'speed_of_light         (make-QL 299792445.8 '(meter) '(second) 0.0))
(list 'stadion                (make-QL 622.0 '(foot) '() 0.0))
(list 'stadium                (make-QL 202.0 '(yard) '() 0.0))
(list 'stokes                 (make-QL 0.0001 '(meter meter) '(second) 0.0))
(list 'survey_mile            (make-QL 320.0 '(rod) '() 0.0))
(list 'tablespoon             (make-QL 0.5 '(fluid_ounce) '() 0.0))
(list 'teaspoon               (make-QL (/ 1.0 3) '(tablespoon) '() 0.0))
(list 'tesla                  (make-QL 1.0 '(weber) '(meter meter) 0.0))
(list 'therm                  (make-QL 1.0e5 '(btu) '() 0.0))
(list 'ton                    (make-QL 2000.0 '(pound) '() 0.0))
(list 'torr                   (make-QL 0.001315789473684210526 '(atmosphere) '() 0.0))
(list 'township               (make-QL 36.0 '(section) '() 0.0))
(list 'troy_ounce             (make-QL 20.0 '(pennyweight) '() 0.0))
(list 'troy_pound             (make-QL 12.0 '(troy_ounce) '() 0.0))
(list 'volt                   (make-QL 1.0 '(joule) '(coulomb) 0.0))
(list 'watt                   (make-QL 1.0 '(joule) '(second) 0.0))
(list 'weber                  (make-QL 1.0 '(volt) '(second) 0.0))
(list 'week                   (make-QL 7.0 '(day) '() 0.0))
(list 'yard                   (make-QL 3. '(foot) '() 0.0))
(list 'year                   (make-QL 365.25 '(day) '() 0.0))
))


;; In your code use UDB as a short name.
(define UDB unicalc-db-huge)  ; comment out this line if you want to debug using a tiny DB
;(define UDB unicalc-db-tiny) ; uncomment   this line if you want to debug using a tiny DB

(generate-report)