;; 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 week5_w_full) (read-case-sensitive #t) (teachpacks ((lib "image.ss" "teachpack" "2htdp"))) (htdp-settings #(#t constructor repeating-decimal #f #t none #f ((lib "image.ss" "teachpack" "2htdp")))))
; new syntax:

; (local [defn1 .... defnN] exp)

; defn can be function def, variable def, or define-struct

; these defns are *only* visible inside the local

;recall sorting:

(define (sorta l)
  (local [(define (sort l)
    (cond
      [(empty? l) l]
      [else (insert (first l) (sort (rest l)))]))

  (define (insert x l)
    (cond
      [(empty? l) (list x)]
      [else (cond
              [(< x (first l)) (cons x l)]
              [else (cons (first l) (insert x (rest l)))])]))
  ] (sort l)))



(define x 1)
(+ (local [(define x 2) (define y (+ x 2))] (+ y 2)) 1)

; sixteenth power
(define (sixteenth i)
  (local [(define double (* i i))
          (define quad (* double double))
          (define eth (* quad quad))]
    (* eth eth)))

;vs.:
;(define (sixteenth i)
; (* i i i i...

;biggest : list-of-numbers -> number
;returns largest number in the list of positive numbers, returns 0 if empty
(define (biggest l) 
  (cond [(empty? l) 0]
        [else 
         (cond [(< (first l) (biggest (rest l))) (biggest (rest l))]
               [else (first l)])]))

(check-expect (biggest (list 1 2 3 4)) 4)
(check-expect (biggest (list 5 3 1)) 5)

(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)))
(time (biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)))
; yikes!

; time(0) = 3
; time(n+1) = time(n) + time(n)
;           = 2 * time(n)
; time(n) = 3*2^n
; n = 100 roughly larger # of steps than # of atoms in known universe

(define (fast-biggest l)
  (cond [(empty? l) 0]
        [else (local [(define bigrest (fast-biggest (rest l)))]
                
         (cond [(< (first l) bigrest) bigrest]
               [else (first l)]))]))

(time (fast-biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15)))
(time (fast-biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16)))
(time (fast-biggest (list 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17)))