/* uses a class to represent a rational as a quotient of
an integer by a positive integer. The member functions implement
arithmetic operators. The function gcd is used to
reduce quotients to lowest terms.*/
#include<iostream.h>
#include<stdlib.h>

struct Rational
{
  int num;
  int denom;
};

void normalize(int int1, int int2, Rational& r);
  //pre: int1 and int2 are integers
  //post: r.num/r.denom has r.denom > 0 and if r.num=0 then r.denom = 1

int gcd(int int1, int int2);
  //computes gcd of int1, int2



void input_rat(Rational& r);
  //post: the rational has a normalized numerator and denominator assigned

void output_rat(Rational& r);


int equal(Rational r1, Rational r2);
//true if r1 = r2


Rational add(Rational r1, Rational r2);
// the normalized sum of r1 and r2


Rational mult(const Rational r1, const Rational r2);

Rational div(const Rational r1, const Rational r2);

int main()
{ Rational r1,r2,r4;

  input_rat(r1);
  cout << "\nThe first rational normalized is :  ";
  output_rat(r1);
  cout << endl;
  input_rat(r2);
  cout << "\nThe second rational normalized is :  ";
  output_rat(r2);
  r4 = add(r1,r2);
  cout << "\nThe sum of the two is: "  ;
  output_rat(r4);
  r4 = mult(r1,r2);
  cout << "\nThe product of the two is: ";
  output_rat(r4);
  r4 = div(r1,r2);
  cout << "\nthe quotient of the two is: ";
  output_rat(r4);

  return 0;
}


void normalize(int int1, int int2, Rational& r)
{ int temp;

  if (int1 == 0)
	int2 = 1;
  else
   if (int2 < 0)
	{ int1 = -int1;
	  int2 = -int2;}
  temp = gcd(int1, int2);
  int1 = int1/temp;
  int2 = int2/temp;

  r.num = int1; r.denom = int2;
}

int gcd(int int1, int int2)
{ int temp1, temp2, temp3;
  temp1 = abs(int1);
  temp2 = abs(int2);
  if (temp1 < temp2)
	{temp3 = temp2; temp2 = temp1; temp1 = temp3;};
  while (temp1 % temp2 != 0)
	 {temp3 = temp2;
	  temp2 = temp1 % temp2;
	  temp1 = temp3;
	 }; //while
   return temp2;
} //gcd



void input_rat(Rational& r)
{ int errcount = 0, int1, int2;

  cout << "\n\nEnter an integer numerator:";
  cin >> int1;
  cout << "Enter an integer denominator:";
  cin >> int2;
  while (int2 == 0)
	{ errcount ++;
	  if (errcount > 3)
	   {cout << "If you insist, the denominator is 0, will cause errors";
		exit (1);}
	  cout << "Denominator 0!! Try again:";
	  cin >> int2;
	} //while

  normalize(int1, int2, r);
}

void output_rat(Rational& r)
{
  cout << r.num << '/' << r.denom;
}

int equal(Rational r1, Rational r2)
{ normalize(r1.num, r1.denom, r1); // just to be sure
  normalize(r2.num, r2.denom, r2);
  return ((r1.num == r2.num) && (r1.denom == r2.denom));
}

Rational add(Rational r1, Rational r2)
// note that the following code is the same as for Add(r1,r2)
{ Rational temp;
  int temp_num, temp_denom;

  temp_num = r1.num*r2.denom + r2.num*r1.denom;
  temp_denom = r1.denom*r2.denom;
  normalize(temp_num, temp_denom, temp);

  return temp;

}


Rational mult(const Rational r1, const Rational r2)
  // similar to +
{ Rational temp; int t1, t2;

  t1 = r1.num*r2.num; t2 = r1.denom*r2.denom;
  normalize(t1,t2,temp);

  return temp;
}


Rational div(const Rational r1, const Rational r2)
{ Rational temp; int t1, t2;

  t1 = r1.num*r2.denom; t2 = r1.denom*r2.num;
  normalize(t1,t2,temp);

  return temp;
}