(**********************************************************************************
 ****************** Assignment 5 **************************************************
 **********************************************************************************)
use("ex5aux.sml");   (* Write here the full path of this file in your computer
                      * For example, "C:/Desktop/ml/ex5aux.sml" for C:\Desktop\ml\ex5aux.sml *)

(****************** Question 3 ****************************************************)

(* 	1.
	Signature: map_n_tree(f, t)
	Type: ('a -> 'b) * 'a n_tree -> 'b n_tree
	Purpose: Apply a given single-parameter function 'f' to the values of all leaves of a given n_tree 't'. 
			 The result is an n_tree with the same structure, containing the corresponding applications of 'f'.  *)
val rec map_n_tree = ... 
(* 	Example 
	val tree1 = N_branch([Leaf 2, N_branch([Leaf 5, Leaf 3, Leaf 8])]);
	map_n_tree((fn x => x * 10), tree1);
 	The last line should return:
	val it = N_branch [Leaf 20,N_branch [Leaf 50,Leaf 30,Leaf 80]] : int n_tree  *)




(* 	2. 
	Signature: map_labeled_n_tree(f, t)
	Type: ('a -> 'b) * 'a labeled_n_tree -> 'b labeled_n_tree
	Purpose: Apply a given single-parameter function 'f' to the values of all nodes of a given labeled_n_tree 't'. 
			 The result is an labeled_n_tree with the same structure, containing the corresponding applications of 'f'.  *)
val rec map_labeled_n_tree = ...
(* 	Example 
	val Ltree1 = L_N_branch(1, [L_Leaf 2, L_N_branch(3, [L_Leaf 5, L_Leaf 3, L_Leaf 8])]);
	map_labeled_n_tree((fn x => x * 10), Ltree1);
 	The last line should return:
	val it = L_N_branch (10,[L_Leaf 20,L_N_branch (30,[L_Leaf 50,L_Leaf 30,L_Leaf 80])]) : int labeled_n_tree 	*)



	
(*	3.
	Signature: preorder_labeled_n_tree(t)
	Type: 'a labeled_n_tree -> 'a list
	Purpose: Collect all elements to a list in a pre-order manner. *)
val rec preorder_labeled_n_tree = ...
(*	Example: 
	preorder_labeled_n_tree(Ltree1);
 	This example should return 
	val it = [1,2,3,5,3,8] : int list *)

	
	
	
(*	4.
	Signature: replace_labeled_n_tree(from_val, to_val, t)
	Type:  ''a * ''a * ''a labeled_n_tree -> ''a labeled_n_tree
	Purpose: replaces all occurences of 'from_val' with 'to_val' in the labeled_n_tree 't'. *)
val replace_labeled_n_tree = ...
(* 	Example 
	replace_labeled_n_tree(3, 30, Ltree1);
 	This example should return 
	val it = L_N_branch (1,[L_Leaf 2,L_N_branch (30,[L_Leaf 5,L_Leaf 30,L_Leaf 8])]) : int labeled_n_tree 	*)

	
	
	
(****************** Question 4*****************************************************)
(*	1.
	Signature: encrypt_seq(k, s)
	Type: int * int seq -> int seq
	Purpose: accept an integer key and a sequence (e.g. a lazy list) of integers, and return
            a sequence of  the encrypted elements of the given sequence, according to the key. *)
val encrypt_seq = ...		
(*	Example: 
	val evens_from_4 = evens_from(4);
	val enc_evens_from_4 = encrypt_seq (1234,  evens_from_4);
	take(enc_evens_from_4, 9); 
	The last line should return
	val it = [8,9,10,11,16,17,18,19,24] : int list 	*)



	
 (* 2.
	Signature: neg_key_seq(k)
	Type: int -> int seq 
	Purpose: repeat the negation of k's digits *)
val neg_key_seq = ...
(* 	Example: 
	take (neg_key_seq(1234), 9);
	This example should return 
	val it = [~4,~3,~2,~1,~4,~3,~2,~1,~4] : int list 	*)



	
(*	3.
	Signature: decrypt_seq(k, es)
	Type: int * int seq -> int seq
	Purpose: decrypt sequence the encrypted sequence 'es' according to key 'k' *)
val decrypt_seq = ...
(*	Example: 
	take (decrypt_seq(1234, enc_evens_from_4) , 9);
 	This example should return
	val it = [4,6,8,10,12,14,16,18,20] : int list	*)