;;; Name: David Evans
;;; Date: 3 February 2004
;;; CS 200 PS2

(load "election.ss")

;;; Question 1a

(define vertical-mid-line 
  (lambda (t) (make-point 0.5 t)))

;;; Question 1b

(define vertical-line
  (lambda (x)
    (lambda (t)
      (make-point x t))))

;;; Question 2a

(define virginia-electorate
  (lambda (pos)
    (+ 0.3 (/ pos 2))))

;;; Question 2b

(define (square x) (* x x))

(define charlottesville-electorate
  (lambda (pos)
    (if (< pos 0.25)
	(- 0.8 (* 10 (square (abs (- pos 0.1)))))
	(if (< pos 0.6)
	        (- 0.575 (- pos 0.25))
		    (+ 0.225 (square (- pos 0.6)))))))

;;; Question 3:

(define (electorate-voters-worker electorate start-position end-position step)
    (if (> start-position end-position)
        0
        (+ (electorate start-position) 
           (electorate-voters-worker electorate (+ start-position step) 
				     end-position step))))

;;; Another way to solve question 3 would be to use for (defined in Lecture 9):

(define (for index stoptest combine next accum)
  (if (stoptest index)
      accum
      (for (next index) stoptest combine next (combine index accum))))

(define (electorate-voters electorate start-position end-position)
  (for start-position 
       (lambda (pos) (> pos end-position)) ;; stop when pos > end-position
       (lambda (pos accum) (+ (electorate pos) accum)) 
       (lambda (pos) (+ pos (/ 1 electorate-steps))) ;; increment by electorate-steps
       0)) ;; initially, accumulator is 0

;;; Question 4:

(define (twice f) (compose f f))

;;; alternately: (define (twice f) (lambda (x) (f (f x))))
;;;          or: (define (twice f) (n-times f 2))

;;; Question 5:

(define (n-times f n)
  (if (= n 0) 
      (lambda (x) x)
      (compose f (n-times f (- n 1)))))
      
;;; Question 6:

; There were lots of easy ways to win the election, which many of you found.  
; The intent of this question was to get you thinking creatively and doing 
; something more interesting than just changing the constants in the provided 
; code, but I guess it wasn't worded clearly enough to encourage you to do
; that.