(* Le texte entre (* *) est du commentaire : Caml l'ignore. *)

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

let fact n =
 if n<0 then 0 else let yo=ref 1 in
 for i=2 to n do yo:= !yo*i; done;
 !yo;;

fact 10;;

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

let somme f n =
 let s = ref 0 in
 for i=1 to n do s:= !s+(f i); done;
 !s;;

let produit f n =
 let p = ref 1 in
 for i=1 to n do p:= !p*(f i); done;
 !p;;

let fact2 = produit (fun x->x);;

fact2 10;;

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

let fibo n = if n<2 then 1 else (
  let a=ref 1 and b=ref 1 in
  for i=2 to n do
   b:= !b + !a;  a:=  !b - !a;
  done;
  !b );;

fibo 10;;

let approx_nb_or () =
 let a=ref 1.0 and b=ref 1.0 and r=ref 1.0 and r2=ref 0.0 in
 while abs_float(!r -. !r2) > 1e-7 do
  let c= !b in b:= c +. !a; a:=c;
  r2 := !r;
  r := !b /. !a;
 done;
 !r;;

approx_nb_or();;
(1. +. sqrt 5.) /. 2. ;;

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

let iter f n x0 = let yo=ref x0 in
 for i=1 to n do yo:= f i !yo done;
 !yo;;

let fact3 n = iter (prefix *) n 1;;

fact3 10;;


(****** Question 5 & 6 ******)

read_line;;
print_endline "bonjour";;
print_int 45;;


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

let blackjack () =
let cagnotte = ref 100 and total=ref 0 and mise=ref 0 in
while !cagnotte>0 do
 print_string "Votre cagnotte est de ";
 print_int !cagnotte;
 print_newline();
 print_string "Votre carte : ";
 total:= 1+random__int 11;
 print_int !total;
 print_newline();
 print_endline "Combien misez-vous ?";
 mise:=read_int();
 while !mise> !cagnotte do
  print_endline "Tu n'as pas assez de sous! Reessaye :";
  mise:=read_int();
 done;
 let continue = ref true in
   while !continue do
    let carte = 1+random__int 11 in
    print_string "Votre carte : ";
    print_int carte;
    total:= !total+carte;
    print_string ". Total : ";
    print_int !total;
    if !total>21 then continue:=false
    else (
     print_string ". Souhaitez-vous continuer ? (o/n)";
     continue := (read_line() = "o")
    );
    print_newline();
   done;
 if !total>21 then (
  print_endline "perdu!";
  cagnotte := !cagnotte - !mise
 )
 else if !total>=17 then (
  print_endline "gagne!";
  cagnotte := !cagnotte + !mise
 )
 else print_endline "petit joueur...";
done;;


(****** Question 8 ******)

let dichotomie f a b = let x = ref a and y = ref b in
 while abs_float(!y -. !x)>1e-7 do let c = 0.5*.(!x +. !y) in
   if (f c) < 0.0 then x:=c else y:=c;
 done;
!x;; 

let yo x = x *. x +. x -. 1.;;
dichotomie yo 0. 2.;;


(****** Question 9 ******)

let factor n = let m = ref n and d = ref 2 in
 while !d * !d <= !m do let puissance = ref 0 in
  while (!m mod !d) = 0 do
   m := !m / !d;
   incr puissance;
  done;
  if !puissance > 0 then (
   print_int !d;
   if !puissance > 1 then (
    print_string "^";
    print_int !puissance;
   );
   print_string " ";
  );
  incr d;
 done;
 if !m > 1 then print_int !m;;

factor 100;;
factor 1001;;
factor 100000001;;
factor 1000000007;;


(****** Question 10 ******)

type fiche = { nom:string; taille:int; poids:float };;
let ma_fiche={nom="moi"; taille=171; poids=62.5; };;
ma_fiche.taille;;

let imc x =
 print_string ("Bonjour " ^ x.nom ^ ", votre indice de masse corporelle est de ");
 print_float (1000. *. x.poids /. float_of_int(x.taille*x.taille));
 print_newline();;

imc ma_fiche;; 


(****** Question 11 ******)

type complexe = { re:float; im:float; };;

let i = { re=0.0; im=1.0; };;

let add x y = { re = x.re +. y.re; im = x.im +. y.im; };;
let sub x y = { re = x.re -. y.re; im = x.im -. y.im; };;
let conj x = { re = x.re; im = 0. -. x.im; };;
let mul x y = { re = (x.re*.y.re)-.(x.im*.y.im); im=(x.re*.y.im)+.(x.im*.y.re); };;
let div x y =
 let mod2 = (y.re*.y.re)+.(y.im*.y.im)
 and tmp=mul x (conj y) in
 { re=tmp.re/.mod2; im=tmp.im/.mod2; };;

mul i i;;
conj i;;
div (sub i (mul i i)) (add i i);;
(***  on a bien (i+1)/2i = (1-i)/2  ***)


(****** Question 12 ******)

let puiss z n = let prod = ref { re=1.0; im=0.0; } in
 for i=1 to n do prod := mul !prod z; done;
 !prod;;

puiss i 12;;

let exp_rapide z n =
 let prod = ref { re=1.0; im=0.0; }
 and mult = ref z
 and e = ref n in
 while !e>0 do
  if !e mod 2 > 0 then prod:= mul !prod !mult;
  e := !e / 2;
  mult := mul !mult !mult;
 done;
 !prod;;

(* ca broute... *)
puiss i 1000003;;

(* ca broute pas *)
exp_rapide i 1000000003;;