let rempliru u i =
	u.(i) <- 15731*u.(i-1) mod 32003;;
let getu u0 = let arr = Array.make 40000 0 in
	arr.(0) <- u0;
	for i=1 to 39999 do
		rempliru arr i
	done;
	arr;;

let uarr = getu 1;;
let u i = uarr.(i);;
let v i j = u (1+i+(j*(j-1)/2));;

u 1000;;
u 10000;;
u 30000;;

let g m n = let adj = Array.make n (Array.make n false) in
	for i=0 to (n-1) do
		adj.(i) <- Array.make n false;
		for j=0  to (i-1)  do
			adj.(i).(j) <- ((v j i) mod m) = 0
		done;
		for j=i+1 to (n-1) do
			adj.(i).(j) <- ((v i j) mod m) = 0
		done
	done;
	adj;;
let aretes g = let n = Array.length g and count = ref 0 in
	for i=0 to (n-1) do
		for j=0 to (n-1) do
			if g.(i).(j) then
				count := !count+1
		done
	done;
	!count/2;;
g 5 10;;
aretes(g 5 10);;
aretes(g 10 50);;
aretes(g 50 250);;

let deg g = let n = Array.length g in
	let count = Array.make n 0 in
	for i=0 to (n-1) do
		for j=0 to (n-1) do
			if g.(i).(j) then
				count.(i) <- count.(i)+1
		done
	done;
	count;;
let degre m n = deg (g m n);;
let max arr = let m = ref arr.(0) in
	for i=1 to (Array.length arr)-1 do
		if arr.(i) > !m
		then m := arr.(i)
	done;
	!m;;
let minLastIndex arr = let im = ref 0 in
	for i=1 to (Array.length arr)-1 do
		if arr.(i) <= arr.(!im)
		then im := i
	done;
	!im;;
let maxFirstIndex arr = let im = ref 0 in
	for i=1 to (Array.length arr)-1 do
		if arr.(i) > arr.(!im)
		then im := i
	done;
	!im;;

max (degre 5 10);;
max (degre 10 50);;
max (degre 50 250);;

minLastIndex (degre 5 10);;
minLastIndex (degre 10 50);;
minLastIndex (degre 50 250);;

maxFirstIndex (degre 5 10);;
maxFirstIndex (degre 10 50);;
maxFirstIndex (degre 50 250);;

(*** 2 Méthode éxacte ***)
open List;;
let rec putall l x rst=
	match l with
		| [] -> rst
		| e::s -> (x::e):(putall s x);;
let rec llen l = match l with
	| [] -> 0
	| e::s -> 1+(llen s);;

let rec parties k l = let n = llen l in
	if k=0 then [ [] ]
	else
		if k=n then [ l ]
		else
			let l0::lr = l in
				(putall (parties (k-1) lr) l0 [])@(parties k lr);;

let rec lin l x = match l with
	| [] -> false
	| e::s -> x=e || (lin s x);;

let tester l g = let n = Array.length g and out = ref true in
	for i = 0 to n-1 do
		for j = 0 to n-1 do
			if g.(i).(j) then
				out := !out && ((lin l i) || (lin l j))
		done
	done;
	!out;;
exception PasDeCouverture;;
let rec testerliste ll g = match ll with
	| [] -> raise PasDeCouverture
	| l::s -> if tester l g
				then l
				else testerliste s g;;
let rec range i n = match n-i with
	| 0 -> []
	| _ -> i::(range (i+1) n);;
	
let rec testall g k = let n = Array.length g in
	let l = range 0 (n-1) in
	try (testerliste (parties k l) g)
	with PasDeCouverture -> testall g (k+1);;

testall (g 5 10) 0;;
testall (g 6 16) 0;;
testall (g 7 20) 0;;

range 0 4;;
parties 1 (range 0 4);;
parties 2 (range 0 4);;
parties 3 (range 0 4);;

putall (parties 3 (range 0 4)) 6 [];;