;; the structure represents a student
;; name is a symbol, 
;; year-birth is a positive integer,
;; GPA is a non-negative real number <= 4.0
 
(define-struct ummstudent (name year-birth GPA))

;; Template:
;;(ummstudent-name student) ....
;;(ummstudent-year-birth student) ....
;;(ummstudent-GPA student) ....

(define JoeSmith
  (make-ummstudent 'JoeSmith 1990 3.45))

(ummstudent-name JoeSmith) 
(ummstudent-year-birth JoeSmith)

(define JaneBrown 
  (make-ummstudent 'JaneBrown 1991 3.25))

;; Contract: ummstudent, ummstudent -> symbol
;; Purpose: the function compares the ages
;; of two students and returns the name of 
;; the one who is older, based on the year of birth
;; If the two students were born in the same year,
;; the function returns a symbol 'BornSameYear
(define (isOlder student1 student2)
  (cond 
    [(= (ummstudent-year-birth student1) (ummstudent-year-birth student2)) 'BornSameYear]
    [(< (ummstudent-year-birth student1) (ummstudent-year-birth student2)) (ummstudent-name student1)]
    [else (ummstudent-name student2)]
  )
)

(check-expect (isOlder JoeSmith JaneBrown) 'JoeSmith)
(check-expect (isOlder JaneBrown JoeSmith) 'JoeSmith)
(check-expect (isOlder JoeSmith JoeSmith)'BornSameYear)


;; Contract: ummstudent -> boolean
;; Purpose: to check whether a given "ummstudent" structure 
;; is well-defined: the name is a symbol, the year 
;; is an integer between 1900 and 2000,
;; the GPA is a number between 0 and 4.0
(define (is-valid student)
  (and 
   (ummstudent? student)
   (symbol? (ummstudent-name student)) ; check name
   (and (integer? (ummstudent-year-birth student)) ; check year-birth
        (<= (ummstudent-year-birth student) 2000)
        (>= (ummstudent-year-birth student) 1900)) 
   (and (real? (ummstudent-GPA student))  ; check GPA
        (<= (ummstudent-GPA student) 4.0)
        (>=  (ummstudent-GPA student) 0.0)
        )
  )
)

(check-expect (is-valid JoeSmith) true)
(check-expect (is-valid (make-ummstudent 5 'TheNineties -3.5)) false)
(check-expect (is-valid (make-ummstudent 'JoeSmith 'TheNineties 3.5)) false)
(check-expect (is-valid (make-ummstudent 'JoeSmith 1990 4.5)) false)

(define students (list JoeSmith JaneBrown (make-ummstudent 'MichaelAnderson 1990 2.95)
                       (make-ummstudent 'KristinJones 1992 3.73)))

;; use predefined functions filter, map, foldl/foldr to accomplish 
;; the following tasks:

;; create a list of students names (in any order)
(map ummstudent-name students)

;; GPA-over-3? ummstudent -> boolean
(define (GPA-over-3? a-student)
  (>= (ummstudent-GPA a-student) 3.0) 
)

;; create a list of students whose GPA is 3.0 or above
(filter GPA-over-3? students)

;; find the average GPA of all students
(/ (foldr + 0 (map ummstudent-GPA students)) (length students))
 
;; create a list of only valid student structures of the ones given 
(filter is-valid (cons (make-ummstudent 2 3 4) students))


(quicksort (list 2 4 7 3 1 3 5) <)

;; use quicksort function to sort the student list by age
;; Can we use isOlder for this? How or why not?

;; is-younger? ummstudent, ummstudent -> boolean
(define (is-younger? student1 student2)
 (< (ummstudent-year-birth student1) (ummstudent-year-birth student2))
)

(quicksort students is-younger?)

;; using any of the given functions, write a function that finds if any 
;; of the students have GPA below 2.0. This function returns true if there
;; is at least one such student and false otherwise

;; using any of the functions, find out how many students have GPA 
;; 3.0 or above