(define (factorial x) 
	(if (< x 2) 1 
	(* x (factorial (- x 1)))))

(define (fact_tail a x)
	(if (< x 2) a
	(fact_tail (* a x)(- x 1))))

(define (rev x)
	(letrec ( ; letrec = let kde definice vidi samy sebe navzajem
		(rev2 (lambda (a x)
			(if(null? x ) a
			(rev2 (cons(car x) a ) (cdr x)))))
	)
	(rev2 '() x)))

(define (mymap f l)
	(if (null? l)
		'()
		(cons (f (car l)) (mymap f (cdr l)))))


(define (myzip . x)
	(if (null? (car x))
		'()
		(cons (mymap car x)  (apply myzip (mymap cdr x)))
	)
)

(define (qs cmp l)
	(if (null? l) l
	(let* ( ; let* = "let" kde dalsi definice vidi ty predchozi
		(pivot (car l))
		(less (filter (lambda (x) (cmp x pivot)) (cdr l)))
		(notless (filter (lambda (x) (not (cmp x pivot))) (cdr l)))
	)
	(append (qs cmp less) (list pivot) (qs cmp notless)) ) )
)

(define (println . l) (for-each display l) (newline))
(println "qsort<: " (qs < '(5 2 9 4 1 5 3)))
(println "qsort>: " (qs > '(5 2 9 4 1 5 3)))

(define (foldl2 f z l) (if (null? l) z (foldl2 f (f (car l) z) (cdr l))))
;puvodni verze s nestandartnim chovanim (vola (f a x) misto (f x a) )
;(define (foldl2 f z l) (if (null? l) z (foldl2 f (f z (car l)) (cdr l))))
;na cviceni me jeste zmatlo to, ze definovana jako foldl navic volala puvodni
;foldl, proto to vypadalo ze jeden pripad se chova jinak.

(define (mymax l) (foldl2 (lambda (x y) (if (> x y) x y)) 0 l))
(println "mymax: " (mymax '(5 2 9 4 1 5 3)))

(define (rev3 x) (foldl2 cons '() x))
(println "rev3: " (rev3 '(5 2 9 4 1 5 3)))