;; 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-beginner-abbr-reader.ss" "lang")((modname week3_w_full) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ())))
; a list-of-numbers is either:
; - empty
; - (cons number list-of-numbers)

; template: 
; (define (fun-for-list-of-numbers numlist)
; (cond [(empty? numlist) ...]
;       [(cons? numlist) ... (first numlist) ... (fun-for-list-of-numbers (rest numlist)) ... ])

; sort : list-of-numbers -> list-of-numbers
; to sort a list of numbers in ascending order
(define (sort lon)
 (cond [(empty? lon) empty]
       [(cons? lon) (insert (first lon) (sort (rest lon)))])
  )

(check-expect (sort empty) empty)
(check-expect (sort (cons 1 (cons 2 empty))) (cons 1 (cons 2 empty)))
(check-expect (sort (cons 2 (cons 1 empty))) (cons 1 (cons 2 empty)))

; insert : number list-of-numbers -> list-of-numbers
; inserts number into list, assuming list is sorted


(define (insert n lon)
  (cond
    [(empty? lon) (cons n empty)]
    [else
     (cond
       [(< n (first lon)) (cons n lon)]
       [(> n (first lon)) 
        (cons (first lon) (insert n (rest lon)))]
       [(= (first lon) n) (cons n lon)])]))

(check-expect (insert 2 empty) (cons 2 empty))
(check-expect (insert 2 (cons 3 empty)) (cons 2 
                                              (cons 3 empty)))
(check-expect (insert 9 (cons 1 (cons 3 (cons 8 (cons 10 empty)))))
              (cons 1 (cons 3 (cons 8 (cons 9 (cons 10 empty))))))

; list shortcuts:
(list 1 2 3)
(cons 1 (cons 2 (cons 3 empty)))
'(1 2 3)