(*********************)
(* Correction du TP5 *)
(*********************)


(**** Question 1 ****)

#open "graphics";;
open_graph "800x600+20+20";;

for i=0 to 255 do for j=0 to 255 do
  set_color (rgb i 0 j); plot i j; done; done;;


(**** Question 2 ****)

let sirp n =
 clear_graph();
 set_color black;
 plot 10 550;
 for i=1 to n do for j=0 to i do
  let (x,y) = (j+10,550-i) in
  if point_color x (y+1) <> point_color (x-1) (y+1) then
   plot x y;
 done; done;;

sirp 512;;   

(**** Question 3 ****)

let coord (x0,x1) width x =
 int_of_float (0.5 +. (float_of_int (width-1)) *. (x-.x0) /. (x1-.x0));;

coord (-1.0,1.0) 800 (-1.0);;
coord (-1.0,1.0) 800 1.0;;
coord (-1.0,1.0) 800 0.5;;

let draw_axes (xmin,ymin,xmax,ymax) =
 let mto x y = moveto (coord (xmin,xmax) (size_x()) x) (coord (ymin,ymax) (size_y()) y)
 and lto x y = lineto (coord (xmin,xmax) (size_x()) x) (coord (ymin,ymax) (size_y()) y)
in
 set_color black;
 mto 0.0 ymin;
 lto 0.0 ymax;
 mto xmin 0.0;
 lto xmax 0.0;;

draw_axes (-2.0,-1.0,1.0,2.0);;

let step (xmin,xmax) n i =
 xmin +. (xmax -. xmin) *. (float_of_int i) /. (float_of_int n);;

step (-1.0,1.0) 200 50;;

let trace (xmin,ymin,xmax,ymax) f n =
  draw_axes (xmin,ymin,xmax,ymax);
  let mto x y = moveto (coord (xmin,xmax) (size_x()) x) (coord (ymin,ymax) (size_y()) y)
  and lto x y = lineto (coord (xmin,xmax) (size_x()) x) (coord (ymin,ymax) (size_y()) y)
in
 mto xmin (f xmin);
 for i=1 to n do let x = step (xmin,xmax) n i in lto x (f x); done;;
 
clear_graph();; 
trace (-6.0,-1.5,6.0,1.5) sin 500;;


(**** Question 4 ****)

let joli () =
 let continue = ref true in
 while !continue do
   let st = wait_next_event [Mouse_motion; Key_pressed] in
   if st.keypressed then continue:=false;
   fill_circle st.mouse_x st.mouse_y 5;
  done;;

let joli2 () =
 let x = ref 0
 and y = ref 0 
 and continue = ref true in
 while !continue do
   let st = wait_next_event [Mouse_motion; Key_pressed] in
   if st.keypressed then continue:=false;
   set_color (rgb (128 + st.mouse_x - !x) 0 (128 + st.mouse_y - !y));
   fill_circle st.mouse_x st.mouse_y 5;
   x := st.mouse_x;
   y := st.mouse_y;
  done;;


(**** Question 5 ****)

type arbre =
| vide
| nd of int*arbre*arbre;;

let rec search x = function
| vide -> false
| nd(y,g,d) ->
  if x=y then true else
  if x<y then search x g else
  search x d;;

let rec insert x = function
| vide -> nd(x,vide,vide)
| nd(y,g,d) -> if x<y then nd(y,insert x g,d)
                      else nd(y,g,insert x d);;

let rec affiche = function
| vide -> ()
| nd(x,g,d) -> affiche g; print_int x; print_string ","; affiche d;;

let rec arbre_of_list = function
| [] -> vide
| t::q -> insert t (arbre_of_list q);;

let trie_list l = affiche (arbre_of_list l);;

trie_list [2;5;3;2;5;3;2;1;0;7];;


(**** Question 6 ****)

let draw_node x y i = 
  set_color white;
  fill_circle x y 16;
  set_color black;
  moveto (x-8) (y-12);
  draw_string (string_of_int i);
  draw_circle x y 16;;

let dessine_arbre= 
 let rec aux x y l = function
 | vide -> ()
 | nd(i,g,d) ->
     set_color black;
     moveto (x-l) (y-40);
     lineto x y;
     lineto (x+l) (y-40);
     draw_node x y i;
     aux (x-l) (y-20) (l/2) g;
     aux (x+l) (y-20) (l/2) d;
in
 aux 400 550 200;;

clear_graph();;
dessine_arbre (arbre_of_list [1;4;2;3;6;1;7;8]);;


  


  
(**** Question 7 ****)

let dead = green;;
let baby = blue;;

let age x = if x=dead || x=white then white else
 if x >= 240*65536 then magenta else x + (rgb 16 0 0);;

let xmin = ref 0;;
let ymin = ref 0;;
let xmax = ref 0;;
let ymax = ref 0;;

let cellule x y = let c = point_color (5*x) (5*y) in
 c <> white && c <> baby;;

let point x y c = set_color c; fill_rect (5*x) (5*y) 5 5;;

let pass1 () =
  for x = !xmin-1 to !xmax+1 do
    for y = !ymin-1 to !ymax+1 do
      let nb_voisins = ref 0 in
      if cellule (x-1) (y-1) then incr nb_voisins;
      if cellule (x+1) (y-1) then incr nb_voisins;
      if cellule (x-1) (y+1) then incr nb_voisins;
      if cellule (x+1) (y+1) then incr nb_voisins;
      if cellule (x) (y+1) then incr nb_voisins;
      if cellule (x+1) (y) then incr nb_voisins;
      if cellule (x-1) (y) then incr nb_voisins;
      if cellule (x) (y-1) then incr nb_voisins;
      if !nb_voisins = 3 && not(cellule x y) then (
        point x y baby;
        if x < !xmin then xmin:=x;
        if y < !ymin then ymin:=y;
        if x > !xmax then xmax:=x;
        if y > !ymax then ymax:=y;
      );
      if (!nb_voisins < 2 || !nb_voisins > 3) && cellule x y then (
        point x y dead;
      );
    done;
  done;;

let pass2 () =
  for x = !xmin-1 to !xmax+1 do
    for y = !ymin-1 to !ymax+1 do
      point x y (age (point_color (5*x) (5*y)));
    done;
  done;;

let init() =
  clear_graph();
  xmin := 100000;
  ymin := 100000;
  xmax := 0;
  ymax := 0;
  let continue = ref true in
  while !continue do
    let st = wait_next_event [Button_down; Key_pressed] in
    if st.keypressed then continue:=false else (
      let (x,y) = (st.mouse_x/5,st.mouse_y/5)
      and c = point_color st.mouse_x st.mouse_y in
      if c=baby then point x y white else point x y baby;
      if x > !xmax then xmax:= x;
      if y > !ymax then ymax:= y;
      if x < !xmin then xmin:= x;
      if y < !ymin then ymin:= y;
    )
  done;;
  
let main() =
  init();
  let cont = ref true
  and pass = ref true in
    while !cont do
     if !pass then pass2() else pass1();
     pass := not (!pass);
     let st = wait_next_event [Button_down; Key_pressed] in
     if st.keypressed then cont:=false;
    done;;


let rapide() =
  clear_graph();
  for i=1 to 300 do point (30+random__int 30) (30+random__int 30) baby done;
  xmin := 30;
  ymin := 30;
  xmax := 60;
  ymax := 60;
  while not key_pressed() do pass2(); pass1(); done;;

rapide();;