;; 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-advanced-reader.ss" "lang")((modname merge-sort) (read-case-sensitive #t) (teachpacks ()) (htdp-settings #(#t constructor repeating-decimal #t #t none #f () #f)))
(define (merge lst1 lst2) (cond
                            [(empty? lst1) lst2]
                            [(empty? lst2) lst1]
                            [(<= (first lst1) (first lst2)) (cons (first lst1) (merge (rest lst1) lst2))]
                            [else (cons (first lst2) (merge lst1 (rest lst2)))]
                            ))

(define (is-sorted? lst) (cond
                           [(empty? lst) true]
                           [(empty? (rest lst)) true]
                           [(> (first lst) (second lst)) #f]
                           [else (is-sorted? (rest lst))]
                           ))

(define (take lst n) (cond
                       [(empty? lst) empty]
                       [(= n 0) empty]
                       [(= n 1) (list (first lst))]
                       [else (cons (first lst) (take (rest lst) (- n 1)))]
                       ))

(define (skip lst n) (cond
                       [(empty? lst) empty]
                       [(= n 0) lst]
                       [else (skip (rest lst) (- n 1))]
                       ))

(define (upper-half lst) (cond
                           [(empty? lst) empty]
                           [else (take lst (floor (/ (length lst) 2)))]
                           ))



(define (lower-half lst) (cond
                           [(empty? lst) empty]
                           [else (skip lst (floor (/ (length lst) 2)))]
                           ))

(define (merge-sort lst) (cond
                           [(empty? lst) lst]
                           [(empty? (rest lst)) lst]
                           [else (merge (merge-sort (upper-half lst)) (merge-sort (lower-half lst)))]
                           ))