;; 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-lambda-reader.ss" "lang")((modname week7_w._fullrkt) (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")))))
; Structural recursion
; right from template

; list-of-numbers is either:
; - empty, or
; - (cons number list-of-numbers)

; max-list : list-of-numbers -> number
; returns the largest element in a list of (positive) numbers
(define (max-list lon) 
  (cond [(empty? lon) 0]
        [else (max (first lon) (max-list (rest lon)))]
  ))

(check-expect (max-list (list 1 2 3)) 3)


; Generative Recursion
; you have to invent the recursive call (using your brilliance)

; factorial : number -> number
; computes n!
(define (factorial n) 
  (cond [(= n 1) 1]
        [else (* n (factorial (- n 1)))])
  )

(check-expect (factorial 5) 120)


; fib : n -> fib(n)
; computes nth fibonacci number where f_n = f_(n-1) + f_n-2)
;                             and f_0 = f_1 = 1
(define (fib n)
  (cond [(= n 0) 1]
        [(= n 1) 1]
        [else (+ (fib (- n 1)) (fib (- n 2)))]
        ))

(check-expect (fib 5) 8)