namespace pars {
  const float Dt=0.1; // l'intervallo di tempo
}

class vett {
  public:
    vett(float x=0., float y=0.) : theX(x), theY(y) {}
    float x() const { return theX; }
    float y() const { return theY; }
    vett operator-() const { return vett(-x(), -y()); } // inverso

  private:
    float theX, theY;
};

vett operator*(const float& s, const vett& v) { // s*v (prodotto per scalare)
  return vett(s*v.x(), s*v.y()) ;
}
vett operator*(const vett& v ,const float& s ) { // v*s (prodotto per scalare e' commutativo)
  return s*v;
}
vett operator+(const vett& a, const vett& b) { // a+b
  return vett(a.x()+b.x(), a.y()+b.y());
}
vett operator-(const vett& a, const vett& b) { // a-b
  return a+(-b);
}
ostream& operator<<(ostream& out, const vett& v) { // cout << v
  out << "("<< v.x() << "," << v.y() << ")" ;
  return out;
}

class palla {
  public:
    palla(float m, vett pos = vett(), vett vel = vett()) 
      : theM(m), thePos(pos), theVel(vel) {}

    float m() const {return theM;}
    vett pos() const { return thePos; }
    vett vel() const { return theVel; }

    void evolvi(const vett& Forza) {
      // qui devo mettere le eq del moto cinematiche: mi serve ( pars::Dt )
      vett a=Forza*(1./m());
      theVel=theVel+a*pars::Dt;
      thePos=thePos+vel()*pars::Dt;
    } 

    void controllaBordi(float minx, float maxx, float miny, float maxy) {
      if (pos().x()<=minx || pos().x() >=maxx) theVel=vett(-vel().x(), vel().y());
      if (pos().y()<=miny || pos().y() >=mayy) theVel=vett(vel().x(), -vel().y());
    }


  private:
    const float theM ; // the mass
    vett thePos, theVel;
};

class scatola {
  public:
    scatola(float minx=0., float maxx=100., float miny=0., float maxy=100.) :
      theMinX(minx), theMaxX(maxx), theMinY(miny), theMaxY(maxy) {
        theP1=palla(1., vett(10,10)); // inizialmente ferma
        theP2=palla(10., vett(20,20)); // inizialmente ferma
      }
    void evolvi() {
      // calcolo la forza risultante su P1 e P2
      vett F1; 
      // gravita' // F1=F1+gravita;
      F1 = F1 + theP1.m()*vett(0.,pars::g);
      // forza elastica // F1=F1+Fel;
      // distanza tra le due palle
      vett dist=theP1.pos()-theP2.pos();
      // Fel=-k*dist
      F1 = F1 + -(pars::k)*dist;
      // idem per P2
      vett F2 = theP2.m()*vett(0.,pars::g);
      F2 = F2 + (pars::k)*dist; // 3o principio dimanica

      // faccio evolvere P1 e P2
      theP1.evolvi(F1);
      theP2.evolvi(F2);

      // controllo se P1 e P2 hanno raggiunto i bordi
      theP1.controllaBordi(theMinX, theMaxX, theMinY, theMaxY);
      theP2.controllaBordi(theMinX, theMaxX, theMinY, theMaxY);
    }

    void display() {
      cout << "P1: " << theP1 << " | P2 = " << theP2 << endl;
    }

  private:
    palla theP1, theP2;
    float theMinX, theMaxX, theMinY, theMaxY;
};


int main(int maxIter = 100) {
  scatola s;
  for (int i=0; i< maxIter; ++i ) {
    s.evolvi();
    s.display();
  }
  return 0;
}