Ajout du test de génération de tables d'addition

Test.ml

@@ -79,6 +79,7 @@ distance_minimale cocylined;;
 print_vecteur 7 (cyclencode cocycl 0b1010);;
 
 (* Essayons de générer une table d'addition *)
+let n = 7;;
 
 type element = Zero | Ap of int;;
 
@@ -147,10 +148,172 @@ print_endline"";
 estTransitif arr;;
 
 
-let n = 7 (* alpha est racine neme de l'unité *);;
-for i=0 to 100_000 do
+let n = 15 (* alpha est racine neme de l'unité *);;
+for i=0 to 100 do
 let arr=randtabl n in
 if estTransitif arr;
 then (for i=0 to n-2 do printalp arr.(i) done;
 print_endline"")
-done;;
+done;;
+
+(* Cette fonction utilise les super formules en partant de 
+ la valeur indiquée *)
+exception ContradictionException of int * int array;;
+exception EmptyException;;
+let pop q = match !q with
+	| [] -> raise EmptyException
+	| e::s -> q:=s;e;;
+let push q e = q:=e::!q;;
+
+(* Renvoie la LISTE des valeurs non associées dans arr *)
+(* Suppose que arr\{-1} est bijective (assurée par l'involutivité de phi) *)
+(* Bien entendu, on oublie le zéro *)
+let missingValues arr =
+	let n = Array.length arr in
+	let rec aux arr i l =
+		if i=0 then l else
+		if (arr.(i)=(-1)) then
+			aux arr (i-1) (i::l)
+		else aux arr (i-1) l
+	in aux arr (n-1) [];;
+	
+let printtbl arr= 
+	let n = Array.length arr in
+	print_string "[";
+	print_int arr.(0);
+	for i=1 to (n-1) do
+		print_string "|";
+		print_int arr.(i)
+	done;
+	print_string "]";;
+let printlst lst = 
+	print_string "[";
+	match lst with
+	| [] -> ()
+	| e::s -> begin
+		print_int e;
+		let rec aux ll = match ll with
+			| [] -> ()
+			| h::t -> print_string ",";print_int h;aux t
+		in aux s end;
+	print_string "]";;
+exception FoundException;;
+let arrmem arr e =
+	let n = Array.length arr in
+	try
+		for i=0 to n-1 do
+			if arr.(i)=e then raise FoundException
+		done;
+		false
+	with FoundException -> true;;
+
+
+let remplis tble k =
+	let n = Array.length tble in
+	let queue = ref [k] in
+	while !queue<>[]
+	do
+		let el = pop queue in
+		(* Test de l'involutivité *)
+		begin 
+		match tble.(tble.(el)) with
+			| -1 -> (tble.(tble.(el)) <- el;push queue tble.(el))
+			| x when x=el -> ()
+			| _ -> raise (ContradictionException(el,tble))
+		end;
+		(* Test de la formule d'opposition *)
+		let opv = (n+tble.(el)-el) mod n in
+		match tble.(n-el) with
+			| -1 -> (tble.(n-el) <- opv;push queue (n-el))
+			| x when x=opv-> ()
+			| _ -> raise (ContradictionException(el,tble))
+	done;;
+	
+let rec cleanTable tble mv = match mv with
+	| [] -> ()
+	| e::s -> tble.(e) <- (-1);cleanTable tble s;;
+
+let rec exploiteVerbose tble =
+	let mv = missingValues tble in
+	print_string "Exploiting ";
+	printtbl tble;
+	print_string " with ";
+	printlst mv;
+	print_endline ".";
+	match mv with [] -> print_string "Raf:";printtbl tble | k::r ->
+	let rec traite tble k mv mm =
+	begin
+		match mm with [] -> print_endline "Fini" | m::rr ->
+		if k<>m then
+		begin
+		cleanTable tble mv;
+		tble.(k) <- m;
+		print_string "m=";
+		print_int m;
+		print_endline ":";
+		try
+			remplis tble k;
+			if arrmem tble (-1)
+			then (* On déscend d'un étage *)
+				(exploite tble;print_endline "pouf";traite tble k mv rr (* Ce n'était pas le bon ... *))
+			else begin
+			print_string "Gtrouvé :";
+			printtbl tble;
+			print_endline ""
+			end
+		with ContradictionException(el,arr) -> (print_string "Contradiction: ";printtbl arr;print_endline "...");
+		traite tble k mv rr (* Ce n'était pas le bon ... *)
+		end
+		else traite tble k mv rr
+	end
+	in traite tble k mv mv;;
+
+let rec exploite tble =
+	let mv = missingValues tble in
+	match mv with [] -> () | k::r ->
+	let rec traite tble k mv mm =
+	begin
+		match mm with [] -> () | m::rr ->
+		if k<>m then
+		begin
+		cleanTable tble mv;
+		tble.(k) <- m;
+		begin
+		try
+			remplis tble k;
+			if arrmem tble (-1)
+			then (* On déscend d'un étage *)
+				(exploite tble)
+			else begin
+			print_string "Gtrouvé :";
+			printtbl tble;
+			print_endline ""
+			end
+		with ContradictionException(el,arr) -> ()
+		end;
+		end;
+		traite tble k mv rr
+	end
+	in traite tble k mv mv;;
+
+let trouve n = 
+	let arr = (Array.make n (-1)) in
+	arr.(0) <- 0;
+	exploite arr;;
+trouve 15;;
+printtbl (Array.make 7 (-1));;
+missingValues (Array.make 7 (-1));;
+let rec f n = missingValues (Array.make n (-1));;
+f 7;;
+
+estTransitif [|Ap(4);Ap(8);Ap(14);Ap(1);Ap(10);Ap(13);Ap(9);Ap(2);Ap(7);Ap(5);Ap(12);Ap(11);Ap(6);Ap(3)|];;
+
+printlst [0;1;2;3];;
+
+for i=4 to 1000 do
+trouve i;
+done;;
+let arr=(Array.make 7 (-1)) in
+	arr.(0) <- 0;
+	arr.(1) <- 3;
+	remplis arr 1;;