;; 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-reader.ss" "lang")((modname week6_m) (read-case-sensitive #t) (teachpacks ((lib "image.ss" "teachpack" "htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "image.ss" "teachpack" "htdp")))))
; biggest: list-of-numbers -> number
; returns largest number in list
(define (biggest numlist)
  (cond [(empty? numlist) 0]
   [else (local [
                 (define bigrest (biggest (rest numlist)))]
    (cond [(< (first numlist) bigrest)
           bigrest]
          [else (first numlist)]))]))

;(time (biggest (list 1)))
; -- (biggest empty) (biggest empty)
;time(1) = time(0) + time(0)
;time (2) = time(1) + time(1)
;         = time(0) + time(0) + time(0) + time(0)
; time(n) = 2^n time(0)
(biggest (list 1 2 3))
;(time (biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)))
;(time (biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)))