;;; banana.scm
;;;
;;; A world with gorillas throwing explosive bananas
;;;
;;; Changes:
;;;   * corrected test case outputs -- Sat Feb 7 00:54:11 EST 2004
;;;   * fixed typo in comment -- Sun Feb  8 21:56:12 EST 2004
;;;

;; Some utility definitions provided to you

(define pi (acos -1))

(define degree2radian
  (lambda (deg)
    (/ (* deg pi) 180.)))


;; Problem 1

; YOUR DOCUMENTATION HERE...
;
(define position
  (lambda (a v u t)
    YOUR-CODE-HERE))

; Test cases
;(position 0 0 0 0) 	; -> 0
;(position 0 0 10 0) 	; -> 10
;(position 0 5 5 5) 	; -> 30
;(position 1 1 1 1)	; -> 2.5
;(position 10 10 10 10)	; -> 610
; YOUR TEST CASES HERE...


;; Problem 2

; Finds first root of az^2 + bz + c = 0
; 
(define root1
  (lambda (a b c)
    YOUR-CODE-HERE))

; YOUR DOCUMENTATION HERE...
;
(define root2
  (lambda (a b c)
    YOUR-CODE-HERE))

; YOUR DOCUMENTATION HERE...
;
(define larger-root
  (lambda (a b c)
    YOUR-CODE-HERE))

; Test cases
;(larger-root 1 0 -4)	; -> 2
; YOUR TEST CASES HERE...


;; Problem 3

; YOUR DOCUMENTATION HERE...
;
(define flight-time
  (lambda (vertical-velocity elevation)
    YOUR-CODE-HERE))

; Test cases
;(flight-time 0 0)	; -> 0
;(flight-time 0 100)	; -> approx 4.5
;(flight-time 100 0)	; -> approx 20.4
;(flight-time 100 100)	; -> 
; YOUR TEST CASES HERE...


;; Problem 4

; YOUR DOCUMENTATION HERE...
;
(define distance 
  (lambda (angle velocity elevation)
    YOUR-CODE-HERE))

; Test cases -- (distance angle velocity elevation)
;(distance 45 0 100)	; -> 0
;(distance 0 10 0)	; -> 0
;(distance 90 10 0)	; -> 0
;(distance 45 10 0)	; -> approx 10.2
;(distance 30 10 0)	; -> approx 8.8
;(distance 90 10 100)	; -> 0
;(distance 45 10 100)	
;(distance 30 10 100)
; YOUR TEST CASES HERE...


;; Problem 5

; YOUR DOCUMENTATION HERE...
;
(define hit?
  (lambda (angle velocity elevation burst-radius target-distance)
    YOUR-CODE-HERE))

; Tests
;(distance 45 10 0)	; -> approx 10.2
;(hit? 45 10 0 1 10)	; -> #t
;(hit? 45 10 0 1 50)	; -> #f
; YOUR TEST CASES HERE...


; game
;
; With your procedures above, we have enough to play the game!
; 
; Note that this procedure uses some gory Scheme internally 
; that you are not yet expected to understand. Treat this as
; a black box and don't worry about the internal details.
;
(define play
  (lambda (separation burst-radius height1 height2)
    (display "G1 (")  (display height1) (display "m high)")
    (display " --- ") (display separation) 
    (display "m  --- G2 (")  (display height2) (display "m high)" )
    (newline)
    (let* ((angle1    (prompt-for-command-expression "Player 1 Angle: "))
	   (velocity1 (prompt-for-command-expression "Player 1 Velocity: "))
	   (angle2    (prompt-for-command-expression "Player 2 Angle: "))
	   (velocity2 (prompt-for-command-expression "Player 2 Velocity: ")))
      (cond ((hit? angle1 velocity1 height1 burst-radius separation)
	     (display "Player 2 destroyed!")
	     (newline))
	    ((hit? angle2 velocity2 height2 burst-radius separation)
	     (display "Player 1 destroyed!")
	     (newline))
	    (else
	     (newline)
	     ; Feedback to player 1
	     (display "Player 1's banana went ")
	     (display (distance angle1 velocity1 height1))
	     (display "m") (newline)
	     ; Feedback to player 2
	     (display "Player 2's banana went ")
	     (display (distance angle2 velocity2 height2))
	     (display "m") (newline)
	     ; Loop
	     (play separation burst-radius height1 height2))))))

; Try it out by evaluating the following: (play 10 1 3 2)
; Enter guesses (in *scheme* buffer) followed by ctrl-x ctrl-e
; Use ctrl-c ctrl-c to terminate.


;; Problem 6

; YOUR DOCUMENTATION HERE...
;
(define find-angle
  (lambda (velocity elevation burst-radius target-distance)
    (find-angle-helper 0 velocity elevation burst-radius target-distance)))

; YOUR DOCUMENTATION HERE...
;
(define find-angle-helper
  (lambda (angle velocity elevation burst-radius target-distance)
    YOUR-CODE-HERE))

; Test cases -- (find-angle velocity elevation burst-radius target-distance) ; fixed Sun Feb  8 21:56:12 EST 2004
(define default-radius 1)
(define default-target 20)
;(find-angle 10 100 default-radius default-target)	; -> 68
; Verify that this angle gives right distance...
;(distance 68 10 100)	; -> approx 20.8
;
;(find-angle 11 100 default-radius default-target)	; -> 71
;(find-angle 10 50 default-radius default-target)
;(find-angle 10 50 default-radius 40)
; YOUR TEST CASES HERE...


;; Problem 7

; Some scheme stuff to communicate with gorilla. Don't
; worry about the details, just the interface
; 
(define tell-gorilla
  (lambda (angle velocity)
    (if (or (not angle) (not velocity))
	 (display (list "Sorry, no angle and velocity works"))
	 (display (list "Throw at" angle "degrees and" velocity "meters/sec")))
    (list angle velocity)))

; Tests
;(tell-gorilla 30 15)
;(tell-gorilla #f 15)
;(tell-gorilla 30 #f)


; A bogus find-throw procedure that 
; simply refuses to find a correct solution, but 
; instead just tells the gorilla anything (not a 
; smart thing for a pet programmer to do!)
;
(define find-throw
  (lambda (elevation burst-radius target-distance)
    (tell-gorilla 45 10)))

;(find-throw 10 default-radius default-target)

; YOUR DOCUMENTATION HERE...
;
(define find-throw
  (lambda (elevation burst-radius target-distance)
    (find-throw-helper 0 elevation burst-radius target-distance)))

; YOUR DOCUMENTATION HERE...
;
(define find-throw-helper
  (lambda (velocity elevation burst-radius target-distance)
    YOUR-CODE-HERE))


; Test cases
;
; A previous test, with fixed velocity
;(find-angle 10 10 1 20)	; -> #f
;
; Now find throw angle and velocity
;(find-throw     10 1 20)	; -> (18 11) - other values may work
; Verify that the suggested angle and velocity goes the distance:
;(distance 18 11 10)
;
; YOUR TEST CASES HERE...


;; Problem 8

; How many bananas in a bundle survive a bounce
;
(define num-survive
  (lambda (num)
    (if (even? num)
	(/ num 2)
	(/ (- num 1) 2))))

; Tests
;(num-survive 5)	; -> 2
;(num-survive 2)	; -> 1
;(num-survive 1)	; -> 0

; YOUR DOCUMENTATION HERE...
;
(define bundle-bounces
  (lambda (num)
    YOUR-CODE-HERE))

; Test cases
;(bundle-bounces 5)	; -> 2
;(bundle-bounces 20)	; -> 4
; YOUR TEST CASES HERE...


;; Problem 9

; YOUR DOCUMENTATION HERE...
;
(define bundle-distance
  (lambda (num angle velocity elevation)
    YOUR-CODE-HERE))

; Test cases
;(distance 0 10 50)		; -> approx 31.9
;(bundle-distance 1 0 10 50)	; -> approx 31.9 (one base case)
;(bundle-distance 0 0 10 50)	; -> 0           (another base case)
;(bundle-distance 5 0 10 50)	; -> approx 31.9
;(bundle-distance 5 90 10 50)	; -> 0
;
;(bundle-distance  2 45 10 50)
;(bundle-distance 20 45 10 50)	; farther
; YOUR TEST CASES HERE...


;; Problem 10

; YOUR DOCUMENTATION HERE...
;
(define find-bundle-throw
  (lambda (num elevation burst-radius target-distance)
    YOUR-CODE-HERE))

; Test cases
; Some previous single-banana throws...
;(find-throw          10 default-radius default-target)
;(find-bundle-throw 1 10 default-radius default-target)
;
; Test - when single banana fails, can a bundle succeed?
;(find-throw           50 default-radius 400)	; -> (#f #f)
;(find-bundle-throw 10 50 default-radius 400)	; -> (73 9)
;
; YOUR TEST CASES HERE...


;; Problem 11

; YOUR DOCUMENTATION HERE...
;
(define find-throw
  (lambda (elevation burst-radius target-distance)
    YOUR-CODE-HERE))