#open "graphics" ;; 

open_graph "" ;;

let rec est_valide = function 
 | [] -> false 
 | [0] -> true 
 | [_] -> false 
 | [_;_] -> false 
 | g::h::d::_ when h<0 or g>=d -> false 
 | [_;_;_] -> true 
 | _::_::q -> est_valide q ;;

let rec reduit l = match l with 
 | [_] -> l 
 | [_;_;_] -> l 
 | g::h::d::k::u::q when h=k -> reduit (g::h::u::q) 
 | g::h::q -> g::h::(reduit q) 
 | _ -> failwith "liste incorrecte" ;;

let p n = 10 * n ;;

let dessine l = 
 clear_graph() ; 
 moveto 0 0 ; 
 let rec aux x y = function 
  | [g] -> lineto (p g) (p y) 
  | g::h::q -> lineto (p g) (p y) ; lineto (p g) (p h) ; aux g h q 
  | _ -> failwith "liste incorrecte" 
 in aux 0 0 l ;; 

(* Q1 *)

let rec cite_valide = function 
 | [] -> true 
 | (g,h,d)::q -> (g<d) & (h>0) & (cite_valide q) ;;

let ma_cite = [(20,20,50);(65,20,75);(10,40,30);(60,50,80)] ;;

let immeuble_valide (g,h,d) = (g<d) & (h>0) ;; 

let cite_valide = for_all immeuble_valide ;;

(* Q2 *)

let rec contour_valide = function 
 | [g;h;d] -> g<d & h>0 
 | g::h::d::q -> g<d & h>=0 & contour_valide (d::q) 
 | _ -> false ;;

contour_valide [10;40;30;20;50;0;60;50;80] ;;

(* Q3 *)

let rec contour_reduit = function 
 | [g;h;d] -> g<d & h>0 
 | g::h::d::h'::q -> g<d & h>=0 & h <> h' & contour_reduit (d::h'::q) 
 | _ -> false ;;

contour_reduit [10;40;30;20;50;0;60;50;80] ;;

(* Q4 *) 

let dessine_contour l = 
 clear_graph() ; 
 let k = 10 in 
 let rec aux x y = function 
  | h::d::q -> lineto x h ; lineto d h ; aux d h q 
  | [] -> lineto x 0 
  | _ -> failwith "liste incorrecte" 
 in moveto (hd l) 0 ; aux (hd l) 0 (tl l) ;;

dessine_contour [10;40;30;20;50;0;60;50;80] ;;

(* Q5 *) 

let rec reduire_contour = function 
 | g::h::d::h'::d'::q when h=h' -> reduire_contour (g::h::d'::q) 
 | g::h::q -> g::h::(reduire_contour q) 
 | [x] -> [x] 
 | _ -> failwith "liste incorrecte" ;;

reduire_contour [10;40;30;40;50;0;60;50;80] ;; 

(* Q6 *) 

let rec insere_immeuble (g,h,d) = function 
 | [] -> [g;h;d] 
 | g'::q when d<g' -> g::h::d::0::g'::q 
 | g'::q when d=g' -> g::h::g'::q 
 | g'::h'::d'::q when g<g' & g'<d & d<d' -> g::h::g'::(max h h')::d::h'::d'::q 
 | g'::h'::d'::q when g<g' & d=d' -> g::h::g'::(max h h')::d'::q 
 | g'::h'::d'::q when g<g' & d>d' -> 
   let q' = insere_immeuble (d',h,d) (d'::q) in g::h::g'::(max h h')::q' 
 | g'::h'::d'::q when g=g' & d<d' -> g::(max h h')::d::h'::d'::q 
 | g'::h'::d'::q when g=g' & d=d' -> g::(max h h')::d::q 
 | g'::h'::d'::q when g=g' & d>d' -> 
   let q' = insere_immeuble (d',h,d) (d'::q) in g::(max h h')::q' 
 | g'::h'::d'::q when g'<g & g<d & d<d' -> g'::h'::g::(max h h')::d::h'::d'::q 
 | g'::h'::d'::q when g'<g & g<d & d=d' -> g'::h'::g::(max h h')::d'::q 
 | g'::h'::d'::q when g'<g & g<d' & d'<d -> 
   let q' = insere_immeuble (d',h,d) (d'::q) in g'::h'::g::(max h h')::q' 
 | g'::h'::d'::q when g'<g & g=d' & d'<d -> 
   let q' = insere_immeuble (d',h,d) (d'::q) in g'::h'::q' 
 | g'::h'::d'::q when g'<d' & d'<g -> 
   let q' = insere_immeuble (g,h,d) (d'::q) in g'::h'::q' 
 | [x] when x=g -> [g;h;d] 
 | [x] when x<g -> [x;0;g;h;d] 
 | _ -> failwith "liste incorrecte" 
;;

let rec contour_of_cite = function 
 | [] -> [] 
 | (g,h,d)::q -> insere_immeuble (g,h,d) (contour_of_cite q) ;;

reduire_contour(contour_of_cite ma_cite) ;;

(* Q7 *) 

let rec latex_of_contour = function 
 
(* 
let latex_of_cite l = 
 latex_of_contour (contour_of_cite l) ;;
*)