#lang scheme
; creates a module, allowing all functions in module to be executed in order

; to run, type mzscheme <file.ss>
; or run mzscheme, and type (load "<file.ss>")
; to compile and execute separately
; mzc --exe <file> <file.ss>
; ./<file>

;; exercise 1
(define (sphereVol r)
  ;; calculate the volume of a sphere of radius r
  (* (/ 4 3) (* 3.14159 (* r r r)) )
)

(define (letDemo)
  (let ( 
	(a 3)
	(b 4)
	)
    (printf "from letDemo~n")
    (printf "value of a is ~a~n" a)
    (printf "value of b is ~a~n" b)
   )
)

;; exercise 3
(define (quadeq a b c) 
  ;; use the quadratic formula
  (let ( 
	(discrim (- (* b b) (* 4 a c)))
	)
      (cond 
       ( (> discrim 0) 
	 (printf "double real roots ~a and ~a~n" 
		 (/ (+ (- 0 b) (sqrt discrim)) (* 2 a))
		 (/ (- (- 0 b) (sqrt discrim)) (* 2 a))
		 ) )
       ( (< discrim 0) 
	 (printf "double complex roots ~a and ~a~n" 
		 (/ (+ (- 0 b) (sqrt discrim)) (* 2 a))
		 (/ (- (- 0 b) (sqrt discrim)) (* 2 a))
		 ) )
       (#t (printf "single root ~a~n" 
		 (/ (+ (- b) (sqrt discrim)) (* 2 a))
		 ) )
       )
      )
)

;; exercise 4
(define (power a b)
  ;; assumes b is a non-negative integer
  (cond 
    ( (= b 0) 1 )
    ( (= b 1) a )
    ( (> b 1) (* a (power a (- b 1))) )
  )
)

;; exercise 5
(define (numZeros aList)
  ;; number of zeros in a simple list
  (if (null? aList) 0
      (if (= 0 (car aList))
	  (+ 1 (numZeros (cdr aList)))
	  (numZeros (cdr aList))
	  )
      )
)

;; exercise 6 
;(define (min a b) (if (< a b) a b) )
;(define (max a b) (if (> a b) a b) )
(define (fVal comparef aList)
  ;; return the comparef-est value in aList, assumes aList is not empty
  (if (null? (cdr aList)) 
      (car aList) 
      (comparef (car aList) (fVal comparef (cdr aList) ) )
      )
)

(define (minMax aList)
  ;; return min and max of a non-empty list as a list of length 2
  (list (fVal min aList) (fVal max aList) ))

(when #t
  (letDemo)
  (printf "test ex. 1:  Volume of a sphere of radius 1 is ~a~n" (sphereVol 1))
  (printf "test ex. 3:  Quadratic equation a=2 b=4 c=3~n") 
  (quadeq 2 4 3)
  (printf "test ex. 4:  2 raised to the power 3 is ~a~n" (power 2 3))
  (printf "test ex. 5:  number of zeros in '(0 2 0 4 0 6) is ~a~n"
	  (numZeros '(0 2 0 4 0 6) ) )
  (let (
	(theAnswer (minMax '(10 -2 0 4 20 6) ) )
	)
    (printf "test ex. 6:  min and max in '(10 -2 0 4 20 6) is ~a and ~a~n"
	  (car theAnswer) (cadr theAnswer))
  )
)