(* LISTA 1 *)

let rec flatten1 lsts =
  if lsts = [] then []
  else (List.hd lsts)@flatten1(List.tl lsts);;

flatten1 [[1;2;4];[6;2];[2;3]];;

let rec count (i,lst) =
  if lst=[] then 0
  else if List.hd lst = i then 1+count(i,List.tl lst)
  else count(i,List.tl lst);;

count (3,[1;2;3;4;5;4;3;2;3;8;3;3]);;
count (3,[]);;

let rec duplicate (ob,i) =
  if i=0 then []
  else  ob::duplicate(ob,i-1);;

duplicate (4,4);;

let rec sqrList lst =
  if lst = [] then []
  else ((List.hd lst) * (List.hd lst))::sqrList(List.tl lst);;

sqrList [1;2;3;7];;

let palindrome lst =
  List.rev lst = lst;;

palindrome [1;2;3;4;5;4;3;2;1];;
palindrome [4;6;9;5;4];;

let rec listLength lst =
  if lst=[] then 0
  else 1+listLength(List.tl lst);;

listLength [1;2;3;4;5;6;3;4];;

let rec listAppend (l1,l2) =
  if l1=[] then l2
  else List.hd l1::listAppend(List.tl l1,l2);;

listAppend ([1;3;5;4;],[2;3;2;3;11]);;


(* LISTA 2 *)


let rec fib1 i =
  if i=0 then 0
  else if i=1 then 1
  else fib1(i-2)+fib1(i-1);;

let rec fib2 i =
  if i=0 then 0
  else if i=1 then 1
  else
    let rec fib3 (i,acc,acc2) =
      if i=0 then acc
      else fib3 (i-1,acc+acc2, acc)
    in fib3 (i-2,1,1);;

(*# fib1 37;;
# fib2 37;;*)

let root3 a =
  let rec help(acc) =
    if abs_float(acc**3. -. a) <= 1E-15 *. abs_float(a) then acc
    else help(acc+.((a/.(acc**2.) -. acc)/.3.))
  in if a >= 1. then help(a/.3.) else help(a);;

root3 27.;;

let (_,_,p1,_,_) = (-2,-1,0,1,2);;
let ( _ ,(p3,_)) = ((1,2),(0,1));;


let rec initsegmet (l1,l2) =
  if l1=[] then true
  else if List.hd l1 = List.hd l2 then initsegment (List.tl l1,List.tl l2)
  else false;;

initsegment ([1;2],[1;3;5;7;3;2;1]);;

let rec replace_nth (lst,n,i) =
  if n=0 then i::(List.tl lst)
  else if n>=List.length lst then raise (Failure "za krotka lista")
  else List.hd lst::replace_nth(List.tl lst,n-1,i);;

replace_nth ([1;2;3;4],3,9);;