;; The first three lines of this file were inserted by DrRacket. They record metadata
;; about the language level of this file in a form that our tools can easily process.
#reader(lib "htdp-intermediate-lambda-reader.ss" "lang")((modname HOFC-exercises) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
(require rackunit)
(require "extras.rkt")


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;;; DATA DEFINITIONS 

;; a Posn is a (make-posn Number Number)
;; TEMPLATE:
;; posn-fn : Posn -> ??
(define (posn-fn p)
  (... (posn-x p) (posn-y p)))

;; A ListOfPosn is one of:
;; -- empty
;; -- (cons Posn ListOfPosn)

;; An IntPosn is a (make-posn Integer Integer)

;; A ListOfIntPosn is one of
;; -- empty
;; -- (cons IntPosn ListOfIntPosn)

;; A ListOfInt is one of
;; -- empty
;; -- (cons Integer ListOfInt)

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;; PROBLEM #1

;; posns-moved-by-posn: ListOfPosn Posn -> ListOfPosn
;; GIVEN: a list of positions and a vector delta represented as a Posn
;; RETURNS: the result of adding the vector delta to each posn in the
;; list
;; EXAMPLE: See test below
;; STRATEGY: <to be filled in>






(begin-for-test
  (check-equal?
    (posns-moved-by-posn (list
                           (make-posn 0 0)
                           (make-posn 1 2)
                           (make-posn 3 6))
      (make-posn -1 -2))
    (list
      (make-posn -1 -2)
      (make-posn 0 0)
      (make-posn 2 4))))

;; notice these values are chosen to be non-degenerate (ie, no
;; coincidences). 

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;; PROBLEM #2

;; <write down the destructor template for IntPosn>

;; good-posns : ListOfIntPosn Integer -> ListOfIntPosn
;; GIVEN: a list of integer positions and an integer x0
;; RETURNS: a list of the positions whose x coordinate is x0
;; EXAMPLE: see test below
;; STRATEGY: <to be filled in>






(begin-for-test
 (check-equal?
  (good-posns (list (make-posn 10 20) (make-posn 30 40) (make-posn 10 22))
             10)
  (list (make-posn 10 20) (make-posn 10 22))))


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;; PROBLEM #3

;; ys-of-x0-points : ListOfIntPosn Integer -> ListOfInteger
;; GIVEN: a list of integer positions and an integer x0
;; RETURNS: a list of the y coordinates of the positions whose x
;; coordinate is x0 
;; EXAMPLE: see test below
;; STRATEGY: <to be filled in>



(begin-for-test
  (check-equal?
    (ys-of-x0-points 
      (list (make-posn 10 20) (make-posn 30 40) (make-posn 10 22))
      10)
    (list 20 22)))

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;; PROBLEM #4

;; vertical-line : ListOfInt Integer -> ListOfIntPosn
;; GIVEN: A list of integers ys and an integer x
;; RETURNS: A list of Posns whose x coordinates are all x and whose y
;; coordinates are the numbers in ys.
;; EXAMPLE: See test below
;; STRATEGY: <to be filled in>



(begin-for-test
  (check-equal?
    (vertical-line
      (list 10 30 40)
      2)
    (list
      (make-posn 2 10)
      (make-posn 2 30)
      (make-posn 2 40))))

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;; PROBLEM #5

;; sum-of-multiples : ListOfNumber Number -> Number
;; GIVEN: a list of numbers lon and a number x
;; RETURNS: the sum of v*x for each element v of lon.





(begin-for-test
  (check-equal? 
    (sum-of-multiples
      (list 2 5 10)
      3)
    (+ 6 15 30)))

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;; PROBLEM #6

;; insert-separators : ListOfString String -> String
;; GIVEN: a list of strings los and a string sep
;; RETURNS: the string obtained by concatenating all the strings in los
;; with the separator in between
;; EXAMPLES: See tests below
;; STRATEGY: <to be filled in>



(begin-for-test
 (check-equal? 
  (insert-separators empty ", ")
  "")
 (check-equal?
  (insert-separators 
   (list "one") ", ")
   "one")
 (check-equal?
  (insert-separators
   (list "one" "two" "three")
   ", ")
  "one, two, three"))