;-----------------------------------------------------
;Fibonacciho postupnost
;-----------------------------------------------------

;vypocita n-ty clen Fibonacciho postupnosti
;naivna viacnasobna rekurzia
;FIB1 :: nat -> nat
(DEFUN FIB1 (N) 
   (COND ((= N 0) 1)
         ((= N 1) 1)
         ((< 1 N)
               (+ (FIB1 (- N 1)) 
                  (FIB1 (- N 2))))
))

;-----------------------------------------------------
;priebezne vytvaranie postupnosti
;FIB2 :: nat -> nat
(DEFUN FIB2 (N) 
       (FIRST (FIB2-AUX N '(1 1)))  
)

;vytvori postupnost Fibonacciho cisel ..
;..od indexu 0 po N (od najvacsieho po najmensi)
;FIB2-AUX :: (nat x [nat]) -> [nat]
(DEFUN FIB2-AUX (N ZOZ) 
   (COND ((< N 2) ZOZ)
         (T (FIB2-AUX (- N 1) 
                      (CONS (+ (FIRST ZOZ) 
                               (FIRST (REST ZOZ)))
                             ZOZ)))
))

;-----------------------------------------------------
;priebezne vytvaranie postupnosti
;FIB3 :: nat -> nat
(DEFUN FIB3 (N)
  (COND ((OR (= N 0) (= N 1))  1)
        (T (FIB3-AUX N 1 1))
))

;pomocna funkcia pre FIB3
;arg. 2 a 3 uchovavaju N-1 a N-2 clen ..
;..Fibonacciho postupnosti
;FIB3-AUX :: (nat x nat x nat) -> nat
(DEFUN FIB3-AUX (N FIB_N-1 FIB_N-2)
    (COND ((= N 2) (+ FIB_N-1 FIB_N-2))
          (T  (FIB3-AUX (- N 1) 
                        (+ FIB_N-1 FIB_N-2) 
                        FIB_N-1))
))