(* ---------- exA ---------- *)

type 'a matrix = 'a list list ;;

let rec count b m =
	match m with
		| [] -> 0
		| []::xs -> 0 + count b xs
		| (v::vs)::xs -> (if (v = b) then 1 else 0) + count b [vs] + count b xs
;;

count 4 [[1; 2; 3]; [4; 5; 1]] ;;
count 1 [[1; 2; 3]; [4; 5; 1]] ;;

(* ---------- exB ---------- *)

let rec first m =
	match m with
		| [] -> []
		| []::xs -> first xs
		
		| [v::vs] -> [v]
		| (v::vs)::xs -> v :: first xs
;;

first [[1; 2; 3]] ;;
first [[1; 2; 3]; [4; 5; 1]] ;;
first [[1; 0; 0]; [2; 0; 0]; [3; 0; 0]; [4; 0; 0]] ;;

(* ---------- exC ---------- *)

let rec rest m =
	match m with
		| [] -> []
		| []::xs -> rest xs
		| [v::vs] -> [vs]
		| (v::vs)::xs -> vs :: rest xs
;;

rest [[1; 2; 3]] ;;
rest [[3]; [4; 6; 6]] ;;
rest [[1; 2; 3]; [4; 5; 1]] ;;
rest [[1; 0; 0]; [2; 0; 0]; [3; 0; 0]; [4; 0; 0]] ;;

(* ---------- exD ---------- *)

let rec returnEl n l =
	match l with
		| [] -> []
		| el::xl -> if (n=0) then [el] else returnEl (n-1) xl
;;

returnEl 0 [1; 2; 3; 4] ;;
returnEl 1 [1; 2; 3; 4] ;;
returnEl 2 [1; 2; 3; 4] ;;

let rec diag m =
	match m with
		| [] -> []
		| []::xm -> []
		
		| [el::xm] -> [el]
		| (el::xl)::xm -> el::(diag (rest xm))
;;

diag [[1; 2; 3]; [4; 5; 1]] ;;
diag [[1; 0; 0]; [0; 2; 0]; [0; 0; 3]; [4; 5; 6]] ;;

(* ---------- exE ---------- *)

let rec trans m =
	match rest m with
		| [] -> []
		| _  -> first m :: trans (rest m)
;;

trans [[1; 2; 3]; [4; 5; 1]] ;;
trans [[1; 0; 0]; [0; 2; 0]; [0; 0; 3]; [4; 5; 6]] ;;

(* ---------- exF ---------- *)