KOLOS SZARP F

//1
//a
let tris_same_shoulders (a:float) (h:float)  =
  let area = (a*h)/2.0
  let circuit_xd =
    let diag = sqrt ( (h*h) + (a/2.0)*(a/2.0))
    2.0*diag + a
  (area, circuit_xd)
//b
let six_corner (a:float) = (3.0* a*a *sqrt(a) )/2.0
printf "exc.1-a %A" (tris_same_shoulders 4.0 2.0)
printf "exc.1-b %A" (six_corner 2.0)
//2--
let rec x_n x n buff=
  if n>0 then x_n x (n-1) (buff+x) else buff
printf "exc.2 %A" (x_n 2 4 0)

//3-
let rec x_M_n x n buff=
  if n>0 then x_M_n x (n-1) buff*x else buff
printf "exc.3 %A" (x_M_n 2 4 1)

//4-
let rec e_s_l list bb =
  match list with
  | x::r -> (e_s_l r (x::rest) )
  | [] -> rest
printf "exc.4 %A" (e_s_l [1;2;3;4;5;6;7;8;9] [])

let rec e_s_l list buff bb =
  match list with
  | x::r -> if bb=true then (e_s_l r (x::buff) false) else (e_s_l r buff true)
  | [] -> List.rev buff
printf "exc.4 %A" (e_s_l [1;2;3;4;5;6;7;8;9] [] true)

//5-
let rec_hr list =
  let bb = true
  list |> List.indexed|> List.filter(fun  (i, x)  -> i%2=0 ) |> List.map (fun (i, x) -> (x))
printf "exc.5 %A" (rec_hr [1;2;3;4;5;6;7;8;9] )

//6-
let rec filter_by_n list buff n =
  match list with
  | x::r -> if x%n=0 then (filter_by_n r (x::buff) n) else (filter_by_n r buff n)
  | [] -> List.rev buff
printf "exc.6 %A" (filter_by_n [1;2;3;4;5;6;7;8;9] [] 3)

//7-
let rec_hr list n = List.filter(fun x -> x%n=0 ) list
printf "exc.7 %A" (rec_hr [1;2;3;4;5;6;7;8;9] 3)

//8-
type ksiazka = {
  tytul : string;
  autor : string;
  data_wydania : string;
  wydawnictwo : string;
  lista_stron : int;
  oprawka_twarda : bool;
}

//9-
let min_max_rec list =
  let rec min list got =
    match list with
    | x::rest -> if x<got then min rest x else min rest got
    | [] -> got
  let rec max list got =
    match list with
    | x::rest -> if x>got then max rest x else max rest got
    | [] -> got
  (min list list.[0], max list list.[0])
printfn "ex.9 %A" (min_max_rec [3;2;1;5;8;2])

//10-
let min_max list = (List.min list, List.max list)
printfn "ex.10 %A" (min_max [3;2;1;5;8;2])

//11-
let average_rec list =
  let rec sum list got=
    match list with
    |x::rest -> sum rest (x + got)
    |[] -> got

  (sum list 0) / (List.length list)

//printfn "ex 11 %A" (average_rec [1;2;3;4])

//12-
let average_high list =
  let sum list = List.fold (+) 0 list
  (float (sum list))/(float (List.length list))
printfn "ex 12 %A" (average_high [1;2;3;4])

//13-
let rec count_less list n count =
  match list with
  | x::rest ->if x<n then count_less rest n (count+1) else count_less rest n count
  |[] -> count
printfn "exc.13 : %A" (count_less [2;3;7;11;4;9] 5 0)

//14-
let less_n list n = list |> List.filter(fun x-> x>=n) |> List.length
printfn "ex.14 : %A" (less_n [2;3;7;11;4;9] 5)