(* Question 5 *)

let rec flat = function 
 | [] -> [] 
 | t::q -> t @ (flat q) ;;

(* Question 6 *)

let rec intervalle i j = 
 if i>j then [] else i::(intervalle (i+1) j) ;;

let list_of_bande h g d m = 
 map (fun j -> m.(h).(j)) (intervalle g d) ;;

(* Question 7 *)

let list_of_zone h b g d m = 
 flat (map (fun i -> list_of_bande i g d m) (intervalle h b)) ;;

(* Question 8 *)

let list_of_bloc k m = let g = 3*(k/3) and h = 3*(k mod 3) in 
 list_of_zone (g) (g+2) (h) (h+2) m ;;

(* Question 9 *)

let bonne_liste l = let l19 = intervalle 1 9 in 
 sort__sort (prefix <) l = l19 ;;

(* Question 10 *)

let l08 = intervalle 0 8 ;;

let bon_sudoku m = 
 let lignes = map (fun i -> list_of_bande i 0 8 m) l08 
 and colonnes = map (fun j -> list_of_zone 0 8 j j m) l08 
 and blocs = map (fun k -> list_of_bloc k m) l08 in 
 for_all bonne_liste lignes && for_all bonne_liste colonnes 
 && for_all bonne_liste blocs ;;

(* variante: for_all bonne_liste (lignes @ colonnes @ blocs) *)

let m = [|
[|1;3;5;2;4;6;8;9;7|];
[|6;9;8;5;3;7;1;2;4|];
[|7;2;4;1;8;9;3;5;6|];
[|8;4;6;7;2;3;5;1;9|];
[|5;7;3;9;1;4;6;8;2|];
[|2;1;9;8;6;5;4;7;3|];
[|4;8;2;3;7;1;9;6;5|];
[|9;6;1;4;5;2;7;3;8|];
[|3;5;7;6;9;8;2;4;1|]
|] ;;

let f = it_list (prefix &) true ;;

(* version 1 *)

let bon_sudoku m = 
 let lignes = map (fun i -> list_of_bande i 0 8 m) l08 
 and colonnes = map (fun j -> list_of_zone 0 8 j j m) l08 
 and blocs = map (fun k -> list_of_bloc k m) l08 in 
 f(map f (map (map bonne_liste) [lignes;colonnes;blocs])) ;; 

(* version 2 *)

let bon_sudoku m = 
 let f1 = fun i -> list_of_bande i 0 8 m 
 and f2 = fun j -> list_of_zone 0 8 j j m 
 and f3 = fun k -> list_of_bloc k m in 
 for_all bonne_liste (flat(map (fun f -> map f l08) [f1;f2;f3])) ;;