-- Exo 1a
x <= y <= z  <=>  x <= y and y <= z

-- Exo 1b
max(x, y) <= z <=> (x >= y and x <= z) or (x < y and y <= z)
               <=> x <= z and y <= z
min(x, y) >= z <=> (x <= y and x >= z) or (x > y ans y >= z)
               <=> x >= z and y >= z

-- Exo 1c
max(x, y) >= z <=> (x >= y and x >= z) or (x < y and y >= z)
               <=> x >= z or y >= z
min(x, y) <= z <=> (x <= y and x <= z) or (x > y ans y <= z)
               <=> x <= z or y <= z

-- Exo 1d
Solution Patrice :
---------------------
IF x <= y THEN
  IF y > z THEN
    IF x <= z THEN -- x <= z < y
      y <-> z
    ELSE -- z < x <= y
      x <- z <- y <- x -- simultanément, faut adapter avec la var aux
    END IF
  ELSE -- x <= y <= z
    NULL ;
ELSE -- x > y
  IF y <= z THEN -- x ? z
    IF x <= z THEN -- y < x <= z
      x <-> y
    ELSE -- y <= z < x
      x <- y <- z <- x
    END IF
  ELSE -- x > y > z
    x <-> z
  END IF
END IF

Solution Sylvie :
--------------------
(Dans X,Y, et Z, on a respectivement A,B,et C au départ)
  if X > Y then
    Echanger X et Y
  end if;
  ------ maintenant X = min(A,B) - Y=max(A,B)
  if Y > Z then
    Echanger Y et Z
  end if;
  ------- maintenant Z = max(Y,Z) = max(A,B,C) : il reste à  
  ------- éventuellement ordonner X et Y
  if X > Y then
    Echanger  X et Y
  end if;

-- Exo 1e
(année mod 400 = 0) or (année mod 4 = 0 and année mod 100 <> 0)

-- Exo 2a
function isTriangle(a, b, c : in Natural) return boolean is
begin
  return a <= b + c and b <= a + c and c <= a + b;
end;

-- Exo 2b
function isRectangledTriangle(a, b, c : in Natural) return boolean is
begin
  return a**2 = b**2 + c**2 or b**2 = a**2 + c**2 or c**2 <= a**2 + b**2;
end;

-- Exo 2c
function min3(a, b, c : in Natural) return boolean is
begin
  if a <= b and a <= c then
    return a;
  elsif b <= c then 
    return b;
  else
    return c;
  end if;
end;

function min3(a, b, c : in Natural) return boolean is
begin
  return Natural'Min(a, Natural'Min(b, c));
end;


-- Exo 3a
function isPerfectSquare_1(n : in Natural) return boolean is
  p : natural;
begin
  p := 1;
  while (p + 1)**2 <= n loop
    p := p + 1;
  end loop

  return p ** 2 = n;
end

-- Exo 3c
function naturalSqrt(n : in Natural) return natural is
  p : natural;
begin
  p := 1;
  while (p + 1)**2 <= n loop
    p := p + 1;
  end loop

  return p;
end


-- Exo 4
function isPrimeNumber_naif(n : Natural) return boolean is
   nbDiviseur : Natural := 0;
begin
   for i in 1..n loop
      if n mod i = 0 then
         nbDiviseur := nbDiviseur + 1;
      end if;
   end loop;

   return n = 2;
end;

function isPrimeNumber_Optimisation_1(n : Natural) return boolean is
   nbDiviseur : Natural := 0;
begin
   i := 2;
   loop
      exit when i**2 >= n;
      if n mod i = 0 then
         return false;
      end if;
      i := i + 1;
   end loop;

   return true;
end;

function isPrimeNumber_Optimisation_2(n : Natural) return boolean is
   nbDiviseur : Natural := 0;
   i : Natural;
begin
   if n = 2 then
      return true;
   end if;

   if n mod 2 = 0 or n = 1then
      return false;
   end if;

   i := 3;
   loop
      exit when  i**2 >= n;
      if n mod i = 0 then
         return false;
      end if;
      i := i + 2;
   end loop;

   return true;
end;

-- Exo 5a
   somme : Natural := 0;
   n : Natural := 0;
   tmp : Natural := 0;
begin
   loop
      get(tmp);
      exit when tmp = 0;
      n := n + 1;
      somme := somme + tmp;
   end loop;

   if n /= 0 then
      put(Float(somme) / Float(n));
   end if;
end;

-- Exo 5b
   max : Natural := 0;
   tmp : Natural;
begin
   loop
      get(tmp);
      exit when tmp = 0;
      if tmp > max then
         max := tmp;
      end if
   end loop;

   put(max);
end;

-- Exo 5c
   max : Natural := 0;
   occ : Natural := 0;
   tmp : Natural := 0;
begin
   loop
      get(tmp);
      exit when tmp = 0;
      if tmp > max then
         max := tmp;
         occ := 1;
      elsif tmp = max then
         occ := occ + 1;
      end if;
   end loop;

   put(max); put(" : "); put(occ);
end;


-- Exo 6a
   a, b, c, d : float;
begin
   get(a); get(b); get(c);
   d := b**2 - 4 * a * c;

   if d = 0 then
      put("1 solution : ");
      put(-b / (2 * a));
   elsif d > 0 then
      put("2 solutions : ");
      put((-b + sqrt(d)) / (2 * a));
      put((-b - sqrt(d)) / (2 * a));
   else
      put("Aucune solution dans R");
   end if;
end;

-- Exo 6b
-- pour d = b**2 - 4*a*c > 0
-- soit   t = -(b + sign(b) * sqrt(b**2 - 4*a*c)) / 2
-- alors r1 = t / a
--    et r2 = c / t  (car r1 * r2 = c / a)
   function sign(x : float) return float is
   begin
      if x < 0 then
         return -1.0;
      else
         return 1.0;
      end if;
   end;

   a, b, c, d : float;
   t : float;
begin
   get(a); get(b); get(c);
   d := b**2 - 4 * a * c;

   if d = 0 then
      put("1 solution : ");
      put(-b / (2 * a));
   elsif d > 0 then
      put("2 solutions : ");
      t = -(b + sign(b) * sqrt(b**2 - 4*a*c)) / 2;
      put(t / a);
      put(c / t);
   else
      put("Aucune solution dans R");
   end if;
end;
-- Exo 7abcd
   type T_IntArray is array (Integer range <>) of Integer;
   procedure PascalTriangle(N : Natural) is
      T : T_IntArray(1..N);
      Last, tmp : Natural;
   begin
      for I in T'Range loop
         T(I) := 0;
      end loop;
      t(1) := 1;
      for I in 1..N loop
         Last := 0;
         for j in 1..i loop
            Tmp := T(J);
            T(J) := last + T(J);
            Last := Tmp;
            put(t(j), 5);
         end loop;
         New_Line;
      end loop;
   end;

-- Exo 8a
b, n : Natural;

while n /= 0 loop
  put(n mod b);
  n = n / b;
end loop;