;; a circle is a (make-circle posn number)
(define-struct circle (center radius))

;; A list-of-circles is
;;  - empty
;;  - (cons circle list-of-circles)

;; EXAMPLES OF DATA

(define locirc1 empty)

(define locirc2 (cons (make-circle (make-posn 3 4) 15)
                      (cons (make-circle (make-posn -2 5) 5)
                            (cons (make-circle (make-posn 50 20) 100) 
                                  empty))))

;; TEMPLATES

;(define (circle-func acirc)
;  (circle-center acirc) ...
;  (circle-radius acirc) ...)
;
;(define (loc-func aloc)
;  (cond [(empty? aloc) ...]
;        [(cons? aloc)
;         ... (circle-func (first aloc))
;         ... (loc-func (rest aloc)) ...]))

;; Write a program large-circles, which consumes a list of circles and returns
;; a list of the circles with radius larger than 10

;; EXAMPLES OF PROGRAM

;(large-circles locirc1) = empty
;
;(large-circles locirc2) = (cons (make-circle (make-posn 3 4) 15)
;                                (cons (make-circle (make-posn 50 20) 100) 
;                                      empty))

;; WRITING THE ACTUAL PROGRAM

;; Start with the template for list-of-circles, and add a contract and purpose, 
;; and customize the name of loc-func

;; large-circles : list-of-circles -> list-of-circles
;; return a list of those circles with radius larger than 10
(define (large-circles aloc)
  (cond [(empty? aloc) ...]
        [(cons? aloc)
         ... (circle-func (first aloc))
         ... (large-circles (rest aloc)) ...]))

;; Use the examples to fill in the empty case, and think about the cons case. 
;; Reading the purpose tells you that (large-circles (rest aloc)) returns
;; the list of large circles in the rest of the list.  So you just need to 
;; decide whether the first circle belongs on that list.  Looking at the template, 
;; you pass (first aloc) to circle-func -- this suggests that circle-func
;; should determine whether a circle is large.  

;; large-circles : list-of-circles -> list-of-circles
;; return a list of those circles with radius larger than 10
(define (large-circles aloc)
  (cond [(empty? aloc) empty]
        [(cons? aloc)
         ... (large? (first aloc))
         ... (large-circles (rest aloc)) ...]))

;; Now, you just need a cond to put the first circle on the list depending
;; on whether or not it is large:

;; large-circles : list-of-circles -> list-of-circles
;; return a list of those circles with radius larger than 10
(define (large-circles aloc)
  (cond [(empty? aloc) empty]
        [(cons? aloc)
         (cond [(large? (first aloc))
                (cons (first aloc) (large-circles (rest aloc)))]
               [else (large-circles (rest aloc))])]))

;; That finishes large-circles.  To finish the program, customize the circle-func 
;; template to implement large?

;; large? : circle -> boolean
;; determine whether circle has radius at least 10
(define (large? acirc)
  (> (circle-radius acirc) 10))

;; Finally, test your program on the example data.

;; --------------------------------------------------------------------------------

;; WHAT A COMPLETE SOLUTION WOULD LOOK LIKE

;; Since this document has mixed demonstration with code, here's what we'd expect
;; as a full solution to this problem written up according to the laws of homework

;; DATA DEFINITIONS

;; a circle is a (make-circle posn number)
(define-struct circle (center radius))

;; A list-of-circles is
;;  - empty
;;  - (cons circle list-of-circles)

;; EXAMPLES OF DATA

(define locirc1 empty)

(define locirc2 (cons (make-circle (make-posn 3 4) 15)
                      (cons (make-circle (make-posn -2 5) 5)
                            (cons (make-circle (make-posn 50 20) 100) 
                                  empty))))

;; TEMPLATES (if we asked for them)

(define (circle-func acirc)
  (circle-center acirc) ...
  (circle-radius acirc) ...)

(define (loc-func aloc)
  (cond [(empty? aloc) ...]
        [(cons? aloc)
         ... (circle-func (first aloc))
         ... (loc-func (rest aloc)) ...]))

;; EXAMPLES OF PROGRAM

;(large-circles locirc1) = empty
;
;(large-circles locirc2) = (cons (make-circle (make-posn 3 4) 15)
;                                (cons (make-circle (make-posn 50 20) 100) 
;                                      empty))

;; THE ACTUAL PROGRAM

;; large-circles : list-of-circles -> list-of-circles
;; return a list of those circles with radius larger than 10
(define (large-circles aloc)
  (cond [(empty? aloc) empty]
        [(cons? aloc)
         (cond [(large? (first aloc))
                (cons (first aloc) (large-circles (rest aloc)))]
               [else (large-circles (rest aloc))])]))

;; large? : circle -> boolean
;; determine whether circle has radius at least 10
(define (large? acirc)
  (> (circle-radius acirc) 10))

;; TESTS

(large? (make-circle (make-posn 3 4) 15))
(large? (make-circle (make-posn -2 5) 5))
(large-circles locirc1)
(large-circles locirc2)