(* 

Name: Kwadwo Amoako Sakyi 
Date: Friday October 4, 2009

*)

type vector = float * float;;
let (vec_zero:vector) = (0.0,0.0);;

let vec_neg (v:vector) = (( ((fst v) *. (-1.)), ((snd v) *. (-1.)) ):vector);;

let vec_mag (v:vector) = sqrt( ((fst v) *. (fst v)) +. ((snd v) *. (snd v)) );;

let vec_add (v1:vector) (v2:vector) =  (((fst v1 +. fst v2), (snd v1 +. snd v2)):vector);;

let vec_sub (v1:vector) (v2:vector) =  (((fst v1 -. fst v2), (snd v2 -. snd v2)):vector);;

let vec_dist v1 v2 = vec_mag(vec_add v1 (vec_neg v2) );;


(* 
helper function for romulus and remus; closer: vector -> vector -> vector -> vector 
returns the closer of vectors v1 and v2 to vx
*)
let closer vx v1 v2 = 
	if ( (vec_dist vx v1) <= (vec_dist vx v2) ) 
		then v1 else v2;;

		
let romulus_iter x v = 
	let len = List.length x in
	if len = 0 then vec_zero else
		let temp = ref (List.nth x 0) in
		for i = 0 to (len-1) do
			temp := closer v !temp (List.nth x i) 
		done;
!temp;;


let rec romulus_rec x v = 
	let closer vx v1 v2 = 
		let a = vec_dist vx v1 in
		let b = vec_dist vx v2 in
		match a with 
		c when c <= b -> v1
		| _ -> v2 in
	match x with
	[] -> vec_zero
	| [x] -> x
	| h::t -> closer v h (romulus_rec t v);;



(* Another version of romulus_rec *)
let rec romulus_rec x v = 
	let vec_dist v1 v2 = 
		vec_mag(vec_add v1 (vec_neg v2) ) in
	let closer vx v1 v2 = 
		let a = vec_dist vx v1 in
		let b = vec_dist vx v2 in
		match a with 
		c when c <= b -> v1
		| _ -> v2 in 
	match x with
	[] -> vec_zero
	| [x] -> x
	| h::t -> closer v h (romulus_rec t v) ;;

	
	
	
let remus_iter f n v = 
match n with 
x when x < 0 -> vec_zero
| _ -> let closer vx v1 v2 = 
		let a = vec_dist vx v1 in
		let b = vec_dist vx v2 in
		match a with 
		c when c <= b -> v1
		| _ -> v2 in 
	let temp = ref (f 0) in
	for i = 0 to n do
		temp := closer v !temp (f i) 
	done;
!temp ;;

let rec remus_rec f n v = 
match n with 
x when x < 0 -> vec_zero
|0 -> (f 0)
| _ -> let closer vx v1 v2 = 
		let a = vec_dist vx v1 in
		let b = vec_dist vx v2 in
		match a with 
		c when c < b -> v1
		| _ -> v2 in  
		closer v (f n) (remus_rec f (n-1) v) ;;

(* print_vec function to print vectors has type. print_vec: vector->unit *)
let print_vec (v:vector) = print_string( "(" ^ 
	string_of_float(fst(v)) ^ 
	"," ^ 
	string_of_float(snd(v)) ^
	")" );;

(* print_vec_list function prints a vector list *)
let print_vec_list vl = 
	let length = List.length vl in
	print_string "[";
	for i = 0 to (length-1) do
		print_vec (List.nth vl i);
		if i != (length-1) then	print_string ";"
			else print_string "";
	done;
	print_string "]"
;;


(* 
vector Examples
*)

let (a:vector) = (1.,1.);;
let (b:vector) = (9.,9.);;
let (c:vector) = (3.,3.);;
let (k:vector) = (20.,20.);;
let (e:vector) = (0.,0.);;
let (g:vector) = (5.,5.);;
let (h:vector) = (6.,6.);;

let (t:vector) = (0.5,0.5);;

let (d:vector) = (11.,11.);;
let (z:vector) = (18.,18.);;

(* You can also declare a vector like this *)
let l = ((8.0, 7.0):vector);;

(* declaration of a list *)
let vec_list = [a;b;h;c;k;e];;


(*	test function f for remus remus functions; f: int -> vector
	Defined here to return the ith vector in alist *)
let f i = 
List.nth vec_list i;;	

(* Testings *)

print_string("The zero vector: vec_zero ");;
print_vec vec_zero;;
print_endline" ";;

print_string("vector a: ");;
print_vec a;;
print_endline" ";;

print_string("vector b: ");;
print_vec b;;
print_endline" ";;

print_string("vector c: ");;
print_vec c;;
print_endline" ";;

print_string("vector d: ");;
print_vec d;;
print_endline" ";;

print_string("vector k: ");;
print_vec k;;
print_endline" ";;

print_string("vector g: ");;
print_vec g;;
print_endline" ";;

print_string("vector h: ");;
print_vec h;;
print_endline" ";;

print_string("vector z: ");;
print_vec z;;
print_endline" ";;

print_string("vector l: ");;
print_vec l;;
print_endline" ";;

print_string("vector t: ");;
print_vec t;;
print_endline" ";;

print_string("Calling vec_neg a returns: ");;
print_vec(vec_neg a);;
print_endline" ";;

print_string("Calling vec_neg b returns: ");;
print_vec(vec_neg b);;
print_endline" ";;

print_string("Calling vec_mag a returns: ");;
print_float(vec_mag a);;
print_endline" ";;

print_string("Calling vec_mag b returns: ");;
print_float(vec_mag b);;
print_endline" ";;

print_string("Calling vec_add a b returns: ");; 
print_vec(vec_add a b);;
print_endline" ";;

print_string("Calling vec_add g h returns: ");; 
print_vec(vec_add g h);;
print_endline" ";;

print_string("vec_list contains vectors: vec_list = [a;b;h;c;k;e] ");;
print_vec_list vec_list;;
print_endline" ";;

print_string("vector t: ");;
print_vec t;;
print_endline" ";;

print_string("Testing romulus_iter vec_list t");;
print_vec(romulus_iter vec_list t);;
print_endline" ";;

print_string("Testing romulus_rec vec_list t");;
print_vec(romulus_rec vec_list t);;
print_endline" ";;


print_string("vec_list contains vectors: vec_list = [a;b;h;c;k;e] ");;
print_vec_list vec_list;;
print_endline" ";;

print_string("vector c: ");;
print_vec c;;
print_endline" ";;

print_string("Testing romulus_iter vec_list c");;
print_vec(romulus_iter vec_list c);;
print_endline" ";;

print_string("Testing romulus_rec vec_list c");;
print_vec(romulus_rec vec_list c);;
print_endline" ";;



print_string("vec_list contains vectors: vec_list = [a;b;h;c;k;e] ");;
print_vec_list vec_list;;
print_endline" ";;

print_string("function f: int -> vector, calling f 2 returns");;
print_vec(f 2);;
print_endline" ";;

print_string("vector k: ");;
print_vec k;;
print_endline" ";;

print_string("vec_list contains vectors: vec_list = [a;b;h;c;k;e] ");;
print_vec_list vec_list;;
print_endline" ";;

print_string("Testing remus_iter f vec_list k returns: ");;
print_vec(remus_iter f 2 k);;
print_endline" ";;

print_string("Testing remus_rec f vec_list k returns: ");;
print_vec(remus_rec f 2 k);;
print_endline" ";;


print_string("vector g: ");;
print_vec g;;
print_endline" ";;

print_string("vec_list contains vectors: vec_list = [a;b;h;c;k;e] ");;
print_vec_list vec_list;;
print_endline" ";;

print_string("Testing remus_iter f 4 g returns: ");;
print_vec(remus_iter f 4 g);;
print_endline" ";;

print_string("Testing remus_rec f 4 g returns: ");;
print_vec(remus_rec f 4 g);;
print_endline" ";;