;; Nicholas Tu (partners with Xinran Zhu, but we worked separately ;;              this weekend because I was away)

;; HW 1

;; *****************************************************************
;; 2.2.3
;; Contract: triangle : number number -> number
;;
;; Purpose: to compute the area of a triangle when given a base and ;;          perpendicular height 
;;          
;; Examples: (triangle 3 4) should produce 6 
;;           (triangle 5 1) should produce 2.5
;;
;; Definition:
 (define (triangle base height) 
   (* 1/2 (* base height)))  
;;
;; Tests: 
 (triangle 3 4) (triangle 5 1)
;; Expected values are expressed directly as follows:
 (= (triangle 3 4) 6)
 (= (triangle 5 1) 2.5)
 
;; ******************************************************************
;; 2.2.5 (part 2 only)
;; Contract: 3 equations:  number -> number
;;
;; Purpose: to formulate three expressions as programs
;;        f(n) = n^2 + 10 
;;        g(n) = (1/2) · n^2 + 20 
;;        h(n) = 2 - (1/n)
;;
;; Examples: (f 2) should produce 14
;;           (f 9) should produce 91
;;           (g 2) should produce 22
;;           (g 9) should produce 60.5
;;           (h 2) should produce 1.5
;;           (h 9) should produce 1.88888...
;;
;; Definitions:
 (define (f n) (+ (* n n) 10))
 (define (g n) (+ (* .5 (* n n)) 20))
 (define (h n) (- 2 (/ 1 n)))
;; 
;; Tests:
 (f 2) (f 9) (g 2) (g 9) (h 2) (h 9)
;; Expected values are expressed directly as follows:
 (= (f 2) 14)
 (= (f 9) 91)
 (= (g 2) 22)
 (= (g 9) 60.5)
 (= (h 2) 1.5)
 (= (h 9) (+ 1 8/9))
 
;; ******************************************************************
;; 2.3.1
;; Contract: tax: num -> num
;;           netpay: num -> num
;;
;; Purpose: - to determine the tax on an employee's gross pay, given
;;          the payment amount and an assumed tax rate of 15%
;;          - to determine the netpay of an employee after tax, 
;;          given how many hours worked and an assumed wage rate
;;          of $12 an hour
;;
;; Examples: (tax 100) should produce 15
;;           (tax 500) should produce 75
;;           (netpay 5) should produce 51
;;           (netpay 8) should produce 81.6
;;
;; Definitions:
 (define (tax n) (* n .15))
 (define (wage h) (* 12 h))  ;;(given in reading)
 (define (netpay n) (- (wage n) (tax (wage n))))
;;
;; Tests:
 (tax 100) (tax 500) (netpay 5) (netpay 8)
;; Expected values are expressed directly as follows:
 (= (tax 100) 15)
 (= (tax 500) 75)
 (= (netpay 5) 51)
 (= (netpay 8) 81.6)
 
;; ******************************************************************
;; 3.1.4
;; Contract: profit: num -> num
;;           revenue: num -> num
;;           cost: num -> num
;;           attendees: num -> num
;; 
;; Purpose: to compute the profit as the difference between revenue 
;;          and costs at some given ticket-price
;;          to compute the revenue, given ticket-price 
;;          to compute the costs, given ticket-price
;;          to compute the number of attendees, given ticket-price
;;
;; Examples: (cost 5) should produce 180
;;           (cost 3) should produce 630
;;           (profit 5) should produce 420
;;           (revenue 4) should produce 1080
;;           (attendees 5) should produce 120
;;
;; Definitions:
 (define (profit ticket-price)
  (- (revenue ticket-price)
     (cost ticket-price)))
 (define (revenue ticket-price)
  (*  (attendees ticket-price) ticket-price))
 (define (cost ticket-price) 
  (* 1.5 (attendees ticket-price)))
 (define (attendees ticket-price)
  (+ 120
     (* (/ 15 .10) (- 5.00 ticket-price))))
;;
;; Tests: 
 (cost 5) (cost 3) (profit 5) (revenue 4) (attendees 5)
;; Expected values are expressed directly as follows:
 (= (cost 5) 180)
 (= (cost 3) 630)
 (= (profit 5) 420)
 (= (revenue 4) 1080)
 (= (attendees 5) 120)
;;
;; ******************************************************************
;; 3.3.2
;; Contract: volume-cylinder: num num -> num
;;           base-area: num -> num
;; 
;; Purpose: This program consumes the radius of a cylinder's base 
;;          disk and its height; it computes the volume of the 
;;          cylinder.  Uses PI = 3.14.
;;
;; Examples: (volume-cylinder 5 2) should return 157
;;           (volume-cylinder 2 4) should return 50.24
;;           (volume-cylinder 3 3) should return 84.78
;;           (volume-cylinder 1 5) should return 15.7
;;           (base-area 5) should return 78.5
;; 
;; Definition:
 (define PI 3.14)
 (define (base-area r) (* PI (* r r)))
 (define (volume-cylinder radius height)
   (* (base-area radius) height))
;;
;; Tests:
 (volume-cylinder 5 2) (volume-cylinder 2 4) (volume-cylinder 3 3)
 (volume-cylinder 1 5) (base-area 5)
;; Expected values are expressed directly as follows:
 (= (volume-cylinder 5 2) 157)
 (= (volume-cylinder 2 4) 50.24)
 (= (volume-cylinder 3 3) 84.78)
 (= (volume-cylinder 1 5) 15.7)
 (= (base-area 5) 78.5)
;;
;; ******************************************************************
;; 3.3.3
;; Contract: area-cylinder: num num -> num
;;           base-perimeter: num -> num
;;           (reusing base-area from 3.3.2)
;;
;; Purpose: The program consumes the radius of the cylinder's base 
;;          disk and its height. Its result is the surface area of 
;;          the cylinder. 
;;
;; Examples: (area-cylinder 5 2) should return 219.8
;;           (area-cylinder 2 4) should return 75.36
;;           (area-cylinder 3 3) should return 113.04
;;           (area-cylinder 1 5) should return 37.68
;;           (base-perimeter 5) should return 31.4
;;
;; Definition: (PI and base-area definitions reused from 3.3.2)
 (define (base-perimeter r) (* 2 (* PI r)))
 (define (area-cylinder radius height) (+ (* 2 (base-area radius))
   (* (base-perimeter radius) height)))
;;
;; Tests:
 (area-cylinder 5 2) (area-cylinder 2 4) (area-cylinder 3 3)
 (area-cylinder 1 5) (base-perimeter 5)
;; Expected values are expressed directly as follows:
 (= (area-cylinder 5 2) 219.8)
 (= (area-cylinder 2 4) 75.36)
 (= (area-cylinder 3 3) 113.04)
 (= (area-cylinder 1 5) 37.68)
 (= (base-perimeter 5) 31.4)
;;
;; ******************************************************************
;; 3.3.4
;; Contract: base-outer-area: num num -> num
;;           inner-area: num num -> num
;;           outer-area: num num num -> num
;;           area-pipe: num num num -> num
;;
;; Purpose: computes the surface area of a pipe, which is an open 
;;          cylinder. The program consumes three values: the pipe's 
;;          inner radius, its length, and the thickness of its wall.
;;
;; Example: (area-pipe 2 3 4) should produce 251.2
;;          (area-pipe 1 6 4) should produce 301.44
;;          (area-pipe 5 8 2) should produce 678.24
;;          (area-pipe 3 6 1) should produce 285.74
;;          (area-pipe 4 1 4) should produce 226.08
;;
;; Definition:
 (define (base-outer-area r t) (- (base-area (+ r t)) (base-area r)))
 (define (inner-area r l) (* (base-perimeter r) l))
 (define (outer-area r l t) (* (base-perimeter (+ r t)) l))
 (define (area-pipe r l t) 
   (+ (+ (inner-area r l) (outer-area r l t))
      (base-outer-area r t)))
;;
;; Tests:
 (area-pipe 2 3 4) (area-pipe 1 6 4) (area-pipe 5 8 2) 
 (area-pipe 3 6 1) (area-pipe 4 1 4)
;; Expected values are expressed directly as follows:
 (= (area-pipe 2 3 4) 251.2)
 (= (area-pipe 1 6 4) 301.44)
 (= (area-pipe 5 8 2) 678.24)
 (= (area-pipe 3 6 1) 285.74)
 (= (area-pipe 4 1 4) 226.08)
;;
;; ******************************************************************
;; Extra Problem
;; Contract: convert: num -> num
;;
;; Purpose: It takes one number as input. If the input is even, we 
;;          square it, and if the number is odd, we return 0. 
;;
;; Examples: (convert 1) should produce 0
;;           (convert 2) should produce 4
;;           (convert 7) should produce 0
;;           (convert 4) should produce 16
;;           (convert 11) should produce 0
;;
;; Unfortunately, it's late and I have absolutely no idea how to do this one.