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(**TP2 : Morpion**)

type marque = { c : bool; p: int * int};;
type grille = marque list;;


(*Question 1*)

let grille1 = [{ c = true; p = (0, 0)};
               { c = true; p = (0, 1)};
               { c = true; p = (0, 2)};
               { c = false; p = (1, 1)};
               { c = false; p = (2, 0)};
               { c = false; p = (2, 2)}
              ];;


let grille2 = [{ c = true; p = (0, 1)};
               { c = false; p = (0, 2)};
               { c = true; p = (1, 0)};
               { c = false; p = (1, 1)};
               { c = true; p = (1, 2)};
               { c = false; p = (2, 0)};
              ];;

let grille3 = [{ c = false; p = (0, 0)};
               { c = true; p = (0, 1)};
               { c = false; p = (0, 2)};
               { c = true; p = (1, 0)};
               { c = false; p = (1, 1)};
               { c = true; p = (1, 2)};
               { c = true; p = (2, 0)};
               { c = false; p = (2, 1)};
               { c = false; p = (2, 2)}
              ];;

(*Question 2*)

let dans_les_bornes = List.for_all (fun {c;p =(x,y)} -> 0<=x && x<=2 && 0<=y && y<=2);;

(*Question 3*)

let existe_symbole g i j = List.exists (fun {c;p =(x,y)} -> x==i&&y==j) g;;

(*Question 4*)

let rec sans_doublons g =
  match g with
  |[]|[_] -> true
  |hd::tl -> if existe_symbole tl (fst hd.p) (snd hd.p) then false
             else sans_doublons tl
;;

(*Question 5*)

let compter =
  List.fold_left (fun (x,y) z -> if z.c then (x+1,y) else (x,y+1)) (0,0)
;;


(*Question 6*)

let bonne_grille g =
  let nb_c,nb_r = compter g in
  dans_les_bornes g && sans_doublons g && (nb_c = nb_r || nb_c = nb_r + 1)
;;

dans_les_bornes grille1;;

(*Question 7*)

exception Grille_invalide;;
let bonne_grille_exn g =
  if bonne_grille g then () else raise Grille_invalide;;

(*Question 8*)
let aux_col g i =
  List.fold_left (fun b j -> b && (existe_symbole g i j)) true [0;1;2]
;;
let aux_line g j =
  List.fold_left (fun b i -> b && existe_symbole g i j) true [0;1;2]
;;
let diag g =
  (List.fold_left (fun b (i,j) -> b && existe_symbole g i j) true [(0,0);(1,1);(2,2)]) || (List.fold_left (fun b (i,j) -> b && existe_symbole g i j) true [(0,2);(1,1);(2,0)])
;;

exception Vrai;;
let gagne g =
  try
  for i = 0 to 2 do
    if (aux_col g i)||(aux_line g i) then raise Vrai
  done;
  diag g
  with Vrai -> true
;;
  

(*Question 9*)
let extraire g b = List.filter (fun x-> x.c == b) g;;


(*Question 10*)

let qui_gagne g =
  try 
    bonne_grille_exn g;
    let g1 = extraire g true in
    let g2 = extraire g false in
    match (gagne g1, gagne g2) with
    |true, false -> Printf.printf "Les croix ont gagnées"
    |false, true -> Printf.printf "Les ronds ont gagnées"
    |_,_-> Printf.printf "Match nul"    
  with Grille_invalide ->  Printf.printf "La grille n'est pas valide"
;;

qui_gagne grille1;;
qui_gagne grille2;;
qui_gagne grille3;;