Stare semestry, niepoukladane

1 files changed, 230 insertions, 0 deletions

diff --git a/Semestr 3/pf/lista2/rozw.ml b/Semestr 3/pf/lista2/rozw.ml
new file mode 100644
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+++ b/Semestr 3/pf/lista2/rozw.ml
@@ -0,0 +1,230 @@
+(* Zadanie 1 *)
+
+let sublists l =
+  let rec backtrack sl = function
+    | [] -> [sl]
+    | hd :: tl -> (backtrack (sl @ [hd]) tl) @ backtrack sl tl
+  in backtrack [] l
+
+
+(* Zadanie 2 *)
+
+(* Znalezione tutaj: https://stackoverflow.com/questions/2710233/how-to-get-a-sub-list-from-a-list-in-ocaml *)
+
+let rec super_sublist b e = function
+  | [] -> failwith "empty list"
+  | hd :: tl ->
+    let tail = if e <= 1 then [] else super_sublist (b - 1) (e - 1) tl in
+    if b > 0 then tail else hd :: tail   
+
+(* Moje rozwiązanie: *)
+
+let rec sublist b e l = 
+  let rec suffix idx l = 
+    if idx = 0 then l else suffix (idx - 1) (List.tl l) in 
+  let rec prefix idx l = 
+    if idx = 0 then [] else (List.hd l) :: (prefix (idx - 1) (List.tl l)) in
+  prefix (e - 1) (suffix b l)
+
+let cycle_with_sub sublist_fun xs n = 
+  sublist_fun n (n + (List.length xs)) (xs @ xs) 
+
+let super_cycle = cycle_with_sub super_sublist
+let cycle = cycle_with_sub sublist
+
+
+(* Zadanie 3 *)
+
+let reverse xs =
+  let rec iter res = function
+    | [] -> res
+    | hd :: tl -> (iter (hd :: res) tl) in
+  iter [] xs
+
+let merge_iter cmp xs ys = 
+  let rec iter xs ys res =
+    match xs with
+      [] -> (reverse ys) @ res
+    | hdx :: tlx ->  
+      match ys with
+        [] -> (reverse xs) @ res 
+      | (hdy :: tly) when cmp hdx (List.hd ys) -> 
+        iter tlx ys (hdx :: res)
+      | (hdy :: tly) -> iter xs tly (hdy :: res) in
+  (reverse (iter xs ys []))
+
+let rec merge cmp xs ys =
+  match xs with
+    [] -> ys
+  | hdx :: tlx ->
+    match ys with
+      [] -> xs
+    | (hdy :: tly) when (cmp hdx (List.hd ys)) -> hdx :: (merge cmp tlx ys)
+    | (hdy :: tly) -> hdy :: (merge cmp xs tly)
+
+let gen_pesimistic ?(f = fun x -> x) range = 
+  let rec iter xs = function
+    | 0 -> xs
+    | (n : int) -> iter ((f n) :: xs) (n - 1) in
+  iter [] range 
+
+let time f x =
+  let t = Sys.time() in
+  let fx = f x in
+  Printf.printf "Execution time: %fs\n" (Sys.time() -. t);
+  fx
+
+let test_merge range =
+  let xs = gen_pesimistic range in
+  let ys = gen_pesimistic range in
+  time (merge (<) xs) ys
+
+let test_merge_iter range =
+  let xs = gen_pesimistic range in
+  let ys = gen_pesimistic range in
+  time (merge_iter (<) xs) ys
+
+let halve xs =
+  let rec iter xs crawl sth = 
+    match crawl with
+      [] -> (sth, xs)
+    | [x] -> (sth, xs)
+    | st :: nd :: tl -> iter (List.tl xs) tl ((List.hd xs) :: sth) in
+  let sth, ndh = iter xs xs [] in
+  ((reverse sth), ndh)
+
+let rec mergesort_generic merge cmp = function
+  | [] -> []
+  | [x] -> [x]
+  | xs -> let sth, ndh = halve xs in 
+    merge cmp (mergesort_generic merge cmp sth) (mergesort_generic merge cmp ndh)
+
+let mergesort = mergesort_generic merge (<)
+let mergesort_with_iter_merge = mergesort_generic merge_iter (<)
+
+let test_mergesort = mergesort [6;4;2;624;4;446;46;3;2346234;623;3246;23;6;3462;346]
+let test_mergesort_with_iter_merge = mergesort_with_iter_merge [6;4;2;624;4;446;46;3;2346234;623;3246;23;6;3462;346]
+
+let range = 10000
+let mergesort_test = gen_pesimistic ~f:(fun x -> range - x) range
+let pesimistic_mergesort_test = gen_pesimistic range
+
+let merge_no_reverse cmp xs ys = 
+  let rec iter xs ys res =
+    match xs with
+      [] -> if ys == [] then res else iter xs (List.tl ys) ((List.hd ys) :: res)
+    | hdx :: tlx -> 
+      match ys with
+        [] -> iter tlx ys (hdx :: res)
+      | hdy :: tly -> 
+        if cmp hdx hdy
+        then iter tlx ys (hdx :: res)
+        else iter xs tly (hdy :: res) in
+  iter xs ys []
+
+
+(* Zadanie 4 *)
+
+let rec map f = function
+  | [] -> []
+  | hd :: tl -> (f hd) :: (map f tl)
+
+let rec perm =
+  let rec iter res pref = function
+    | [] -> res
+    | hd :: tl -> 
+      let perms = map (fun ys -> hd :: ys) (perm (pref@tl)) in
+      iter (res @ perms) (pref @ [hd]) tl in function
+    | [] -> [[]]
+    | xs -> iter [] [] xs
+
+let rec flatmap f = function
+  | [] -> []
+  | hd :: tl -> (f hd) @ (flatmap f tl)
+
+let rec perm_flat = 
+  let rec iter res x pref = function
+    | [] -> (pref@[x]) :: res
+    | hd :: tl -> 
+      iter ((pref@(x :: hd :: tl)) :: res) x (pref@[hd]) tl in function
+    | [] -> [[]]
+    | hd :: tl -> 
+      flatmap (iter [] hd []) (perm_flat tl)
+
+
+(* Zadanie 5 *)
+
+let suffixes xs =
+  let rec iter res = function
+    | [] -> [] :: res
+    | hd :: tl -> iter ((hd :: tl) :: res) tl in
+  reverse (iter [] xs)
+
+let prefixes xs = reverse (map reverse (suffixes (reverse xs)))
+
+(* Zadanie 6 *)
+
+type 'a clist = { clist : 'z. ('a -> 'z -> 'z) -> 'z -> 'z }
+
+let cnil = { clist = fun f z -> z }
+let ccons x xs = { clist = fun f z -> f x (xs.clist f z) }
+let map g xs = { clist = fun f z -> xs.clist (fun a z -> f (g a) z) z } 
+let append xs ys = { clist = fun f z -> xs.clist f (ys.clist f z) }
+let clist_to_list xs = xs.clist (fun x xs -> x :: xs) [] 
+(* let prod xs ys = fun f z -> { clist = fun f z -> xs.clist ( ) z }  *)
+
+let prod xs ys = { clist = fun f z -> xs.clist (fun a z -> ys.clist (fun b zz -> f (a, b) zz) z) z }
+
+(* 'a clist -> 'b clist -> ('b -> 'a) clist *)
+(* let list_pow xs ys = { clist= fun f x -> } *)
+
+(* let pow f1 f2 = { cnum = fun f x -> (f2.cnum (mul f1) one).cnum f x } *)
+
+let ccar xs = List.hd (clist_to_list xs)
+
+(* Zadanie 7 *)
+
+type cbool = { cbool : 'a. 'a -> 'a -> 'a }
+type cnum = { cnum : 'a. ('a -> 'a) -> 'a -> 'a }
+
+let even n =
+  { cbool = fun tt ff -> fst (n.cnum (fun (a, b) -> (b, a)) (tt, ff))}
+
+let ctrue = 
+  { cbool = fun a b -> a}
+let cfalse = 
+  { cbool = fun a b -> b}
+let cand f1 f2 a b = f1.cbool (f2.cbool a b) b
+let cor f1 f2 a b = f1.cbool a (f2.cbool a b)
+let cbool_of_bool b = if b then ctrue else cfalse
+let bool_of_cbool f = f.cbool true false
+
+let zero = { cnum = fun f x -> x }
+
+let succ fn = { cnum = fun f x -> fn.cnum f (f x) }
+let add f1 f2 = { cnum = fun f x -> f1.cnum f (f2.cnum f x) }
+let mul f1 f2 = { cnum = fun f x -> f1.cnum (f2.cnum f) x }
+
+let one = succ zero
+let pow f1 f2 = { cnum = fun f x -> (f2.cnum (mul f1) one).cnum f x }
+
+let rec cnum_of_int = function
+  | 0 -> zero
+  | n -> succ (cnum_of_int (n - 1))
+let is_zero f = 
+  let g x = x + 1 
+  in if (f.cnum g 0) = 0 then true else false
+let int_of_cnum f = f.cnum (fun x -> x + 1) 0
+
+let two = succ one
+let three = succ two
+let four = succ three
+let five = succ four
+
+let func x = x * 2
+
+let pred n = { cnum = fun f x -> fst (n.cnum (fun (a, b) -> (b, f(b))) (x, x)) }
+
+let ctail xs = { clist = fun f z -> fst (xs.clist (fun a (z1, z2) -> (z2, f a z2)) (z, z)) }
+
+let length xs = xs.clist (fun a z -> z + 1) 0
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