//developpement de la classe Rational
#include <iostream>
#include <cmath>

using namespace std;

class Rational {
  //membres publiques 
  public:
         
    //constructeurs
    Rational();     //constructeur par defaut (0 parametres)
    Rational(int num);   //constructeur avec 1 parametres  
    Rational(int num, int den);   //constructeur avec 2 parametres  
    Rational(const Rational &r);     //constructeur de copie
    
    //destructeur
    ~Rational();
    
    //fonctions d'access
    int GetNum() const;
    int GetDen() const;
    void SetNum(int num);
    void SetDen(int den);
    
    //methodes publiques
    double Convert() const;    
    void Invert();
    void Print() const;
    void Reduce();
    
    //operateurs surchages
    Rational operator+(const Rational &) const;
    Rational operator-() const;
    Rational operator-(const Rational &) const;
    Rational operator*(const Rational &) const;  
    Rational operator/(const Rational &) const;
    bool operator==(const Rational &) const; 
    bool operator<(const Rational &) const; 
    bool operator<=(const Rational &) const; 
    bool operator>(const Rational &) const; 
    bool operator>=(const Rational &) const; 
    
  //membres privees
  private:
    //donnees privees
    int num;
    int den;
    
    //methodes privees
    
};   //n'oubliez pas le ;

//constructeur par defaut
Rational::Rational() {
  num = 0;
  den = 1;
  cout << "Un nombre Rational a ete cree par defaut." << endl;
}
//constructeur avec 1 parametre
//les deux constructeurs (fonctions) suivants sont equivalents
/*Rational::Rational(int n) {
  num = n;
  den = 1;
  cout << "Un nombre Rational a ete cree; denom. = 1." << endl;
}
*/
Rational::Rational(int n): num(n), den(1) {
  cout << "Un nombre Rational a ete cree; denom. = 1." << endl;
}
//constructeur avec 2 parametres
//les deux constructeurs (fonctions) suivants sont equivalents
/*Rational::Rational(int n, int d) {
  num = n;
  den = d;
  Reduce();
  cout << "Un nombre Rational a ete cree." << endl;
}
*/
Rational::Rational(int n, int d): num(n), den(d) {
  Reduce();
  cout << "Un nombre Rational a ete cree." << endl;
}

//constructeur de copie
//les deux constructeurs (fonctions) de copie suivants sont equivalents
/*Rational::Rational(const Rational &r) {
  num = r.num;
  den = r.den;
  cout << "Un nombre Rational a ete copie." << endl;
}
*/
Rational::Rational(const Rational &r): num(r.num), den(r.den) {
  cout << "Un nombre Rational a ete copie." << endl;
}

//destructeur    
Rational::~Rational() {
  cout << "Un nombre Rational a ete detruit." << endl;
}

//fonctions d'acces
int Rational::GetNum() const {
  return num;
}

int Rational::GetDen() const {
  return den;
}

void Rational::SetNum(int n) {
  num = n;
}

void Rational::SetDen(int d) {
  den = d;
}

//algorithme d'Euclide pour trouver le plus grand diviseur commun
void Rational::Reduce() {
  int m = abs(num);
  int n = abs(den);
  if (m<n) {
    int temp = m;
    m = n;
    n = temp;
  }  
  int r;   
  while (n>0) {
    r = m % n;
    m = n;
    n = r;
  }
  int gdc = m;
  
  num = abs(num) / gdc;
  if (num*den<0) num = -num;
  den = abs(den) / gdc;        
}

double Rational::Convert() const {
  return double(num) / den;
}

void Rational::Invert() {
  int temp = num;
  num = den;
  den = temp;
}

void Rational::Print() const {
  cout << num << '/' << den << endl;
}

//surcharge des operateurs
//N.B. : declaration differente pour les methodes
//qui ne sont pas membre de la classe !
Rational Rational::operator+(const Rational &q) const {
  int n, d;
  n = num*q.den + den*q.num;
  d = den*q.den;
  Rational res = Rational(n,d);
  return res;
}
Rational Rational::operator-() const {
  int n, d;
  n = -num;
  d = den;
  Rational res = Rational(n,d);
  return res;
}
Rational Rational::operator-(const Rational &q) const {
  int n, d;
  n = num*q.den - den*q.num;
  d = den*q.den;
  Rational res = Rational(n,d);
  return res;
}  
Rational Rational::operator*(const Rational &q) const {
  int n, d;
  n = num * q.num;
  d = den * q.den;
  Rational res = Rational(n,d);
  return res;
}
Rational Rational::operator/(const Rational &q) const {
  int n, d;
  n = num*q.den;
  d = den*q.num;
  Rational res = Rational(n,d);
  return res;
}    
bool Rational::operator==(const Rational &q) const {
  return (num*q.den == den*q.num);
}    
bool Rational::operator<(const Rational &q) const {
  return (num*q.den < den*q.num);
} 
bool Rational::operator<=(const Rational &q) const {
  return (num*q.den <= den*q.num);
} 
bool Rational::operator>(const Rational &q) const {
  return (num*q.den > den*q.num);
} 
bool Rational::operator>=(const Rational &q) const {
  return (num*q.den >= den*q.num);
}

int main() {
  Rational q;
  int num, den;
  cout << "Entrez un nombre Rational (fraction) ! " << endl;
  cout << "numerateur : ";
  cin >> num;   q.SetNum(num);
  cout << "denominateur : ";
  cin >> den;  q.SetDen(den);
  q.Reduce();
  cout << "La fraction est : ";
  q.Print();
  cout << "et sa valeur decimal : " << q.Convert() << endl;
  
  cout << endl;
  cout << "Operations arithmetiques avec Rational" << endl;
  Rational a(21, 9);
  cout << "a = ";
  a.Print();
  Rational b(6, 36);
  cout << "b = ";
  b.Print();
  Rational s = a+b;
  cout << "a + b = ";
  s.Print();
  Rational d = a-b;
  cout << "a - b = ";
  d.Print();
  Rational p = a*b;
  cout << "a * b = ";
  p.Print();
  Rational r = a/b;
  cout << "a / b = ";
  r.Print();
  cout << "a / b (decimal) = " << r.Convert() << endl;
  Rational t = -a;
  cout << "-a = ";
  t.Print();
  Rational u = a;     //copie
  cout << "u = ";
  u.Print();
  
  cout << endl;
  cout << "Operations logiques avec Rational" << endl;
  if (a==b) cout << "a et b sont egales !" << endl;
  else cout << "a et b sont differentes !" << endl;
  if (a<b) cout << "a est plus petite !" << endl;
  if (a>b) cout << "a est plus grande !" << endl;
    
  //avec un pointeur
  cout << endl;
  cout << "Rational avec un pointeur" << endl;
  Rational *x;
  x = new Rational;
  x->SetNum(5);
  x->SetDen(13);
  cout << "x = ";
  x->Print();
  cout << "x (decimal) = " << x->Convert() << endl;
  delete x;

  return 0;
}