#lang racket

;; for n=100
;; iterative version takes roughly 0.008 milliseconds.
;; recursive version does not seem like it will finish any time soon.
;; for n=50
;; iterative version takes roughly 0.003 milliseconds in drracket
;; recursive version has not yet finished executing after a couple minutes, and I got bored.
;; for n=25.
;; iterative version takes 0.002ms
;; recursive version takes 46.5 ms
;; yeah. that's big. okay. this shit's important.
;; I wonder how it would be with memoization.


(define-syntax-rule (meas form)
  (let ([my-time (current-inexact-milliseconds)])
    (let ([res form])
      (- (current-inexact-milliseconds) my-time))))


(define (recursive n)
    (if (< n 3)
        n
        (+ (recursive (- n 1))
           (* 2 (recursive (- n 2)))
           (* 3 (recursive (- n 3))))))
(define (iter a b c n)
  (if (<= n 0)
      c
      (iter b c (+ c (* 2 b) (* 3 a)) (- n 1))))
(define (iter-start n)
  (iter 0 1 2 (- n 2)))

(define (ex-1-11 n)
  (let loop ((i n))
    (if (< i 2)
        #t
        (if (= (recursive i) (iter-start i))
            (loop (- i 1))
            (begin 
              (display "UNEQUAL!")
              (displayln i))))))