#lang racket
(require (lib "trace.ss"))

; ------------------Recursivitate pe stivă------------------
(define (fact-stack n)
  (if (zero? n)
      1
      (* n (fact-stack (- n 1)))))

;(trace fact-stack)
;(fact-stack 4)

; ------------------Recursivitate pe coadă------------------
(define (fact-tail n)
  (fact-tail-helper n 1))

(define (fact-tail-helper n acc)
  (if (zero? n)
      acc
      (fact-tail-helper (- n 1) (* n acc))))

(trace fact-tail-helper)
(fact-tail 10)

; ------------------Recursivitate arborescentă------------------
(define (fibo-stack n)
  (if (< n 2)
      n
      (+ (fibo-stack (- n 1)) (fibo-stack (- n 2)))))

;(trace fibo-stack)
;(fibo-stack 5)
;(fibo-stack 40) ;;  deja incepe sa dureze mult

(define (fibo-tail n)
  (fibo-tail-helper n 0 1))

(define (fibo-tail-helper n a b)
  (if (zero? n)
      a
      (fibo-tail-helper (sub1 n) b (+ a b))))

; fibo(0) = 0, fibo(1) = 1
  
;(trace fibo-tail-helper)
;(fibo-tail 5)

;(helper 5 0 1)
;(helper 4 1 1)
;(helper 3 1 2)
;(helper 2 2 3)
;(helper 1 3 5)
;(helper 0 5 8)
;0 1 1 2 3 5
;(map fibo-tail '(0 1 2 3 4 5 6 7))
;(fibo-tail 100000)

; ------------------Recunoaștere tip de recursivitate------------------
(define (g L result)
  (cond ((null? L)        result)
        ((list? (car L))  (g (cdr L) (append (g (car L) '()) result))) ; evaluare aplicativă
        (else             (g (cdr L) (cons (car L) result)))))

(trace g)
(g '(1 2 (3 4) (5 (6 7))) '())