import corejava.Console;
import java.lang.Integer;
import java.lang.String;


////////////////////////////////////////////////////////////////////////////////////////////////////////
//Class Rational-provides functions for performing arithmetic with fractions-rational 		      //
//numbers.It provides functions for addition,subtraction,multiplication and comparision of	      //
//two rational numbers.This class provides the following functions.				      //
//Public class Rational{									      //
//	public Rational(int numeratorval,int denominatorval)	//Initiallizing Cosntructor	      //	
//	public Rational()					//Default Constructor		      //
// 	public void getnumdenom(int numeratorval,int denominatorval)//initiallizes the numerator and  //
//                                                              //denominator of a rational object    //
//      public Rational Addition(Rational r1,Rational r2)	//Addition of 2 Rational numbers      //
//	public Rational Subtraction(Rational r1,Rational r2)	//Subtraction of 2 Rational numbers   //
//	public Rational Multiplication(Rational r1,Rational r2)	//Multiplication of 2 Rational numbers//
//	public Rational Comparision(Rational r1,Rational r2)	//Comparision of 2 Rational numbers   //
//	public void toString(Rational r1)			//forms a string with the Numerator   //
//								//and denominator of r1,with "/" in b/w/
//	private int gcf (int value1, int value2)		//obtains the gcd of 2 Rational numbers/
//	}											      //
////////////////////////////////////////////////////////////////////////////////////////////////////////
public class Rational{

   //instance variables
   private int numerator;			//numerator of the Rational number
   private int denominator;			//denominator of the Rational number
   
   /////////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :Rational(int numeratorval,int denominatorval)				  //
   //Description    :Calls the gcf function to calculate the greatest common divisor of           //   
   //                the inputs-nummeratorval and the denominatorval.                             //
   //		     This function is an Initiallizing constructor function that initializes an   //
   //                object with an initial numerator(i.e numeratorval divided by the greatest    //
   //		     common divisor) and denominator(i.e. denominatorval divided by the greatest  //
   //		     common divisor).This division by the greatest common divisor is done to reduce/ 
   //		     the fraction to lowest terms						  //
   //Inputs	    :numeratorval-an integer which specifies the numerator. 			  // 
   //		     denominatorval-an integer which specifies the denominator  		  //
   //Outputs	    :None					   	                          //
   //Local Variables:None  									  //
   //Author	    :Lakshmi Anumolu								  //
   /////////////////////////////////////////////////////////////////////////////////////////////////
   
   public Rational(int numeratorval,int denominatorval){
  	
	//Call the gcd function to calculate the greatest common divisor of 
	//the nummerator and the denominator
	int greatestcommondivisor=gcf(numeratorval,denominatorval);
	
	//Reduce the numerator and denominator to the lowest terms.
	numerator=numeratorval/greatestcommondivisor;
	denominator=denominatorval/greatestcommondivisor;
   }
   
   /////////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :Rational()									  //
   //Description    :Default constructor that sets the private variables to default values	  //
   //		     sets the numerator to zero,and denominator to 1,So number is zero.		  //
   //Inputs	    :None									  //
   //Outputs	    :None					   	                          //
   //Local Variables:None  									  //
   //Author	    :Lakshmi Anumolu								  //
   /////////////////////////////////////////////////////////////////////////////////////////////////
   public Rational(){
  	numerator=0;			//initiallise the numerator to zero
	denominator=1;			//initiallise the denominator to one
   }

   /////////////////////////////////////////////////////////////////////////////////////////////////
   //Title          : int gcf(int value1,int value2)					 	  //
   //Description    : Private function to find the greatest common divisor of two positive numbers//
   //Inputs         : value1-integer specifies the numerator-value1 > 0				  //
   //		      value2 -integer specifies the denominator-value2 > 0			  //
   //Outputs        : value1-integer-Greatest Common divisor of the two positive numbers	  //
   //Local Variables: temp-an integer storing the temporary value while swapping 2 numbers        //			
   //Author	    : Nancy McCracken								  //
   /////////////////////////////////////////////////////////////////////////////////////////////////
   private int gcf (int value1, int value2){	
        int temp;
	//continue till value1 becomes zero
        while (value1> 0)
        {
           if (value1< value2) { 
		//swap both numbers if the first is less then the second
		temp=value1; 		//temp holds the temporary value during the swapping process
		value1=value2; 
		value2=temp; 
 		}
             value1 = value1 - value2; //subtract the second number from the first
        }
        return value2;   //value2 is the gcd of the 2 numbers
   }
   

   /////////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :void getnumdenom(int numeratorval,int denominatorval){                       //
   //Description    :Calls the gcf function to calculate the greatest common divisor of           //   
   //                the inputs-nummeratorval and the denominatorval.                             //
   //		     This function sets the numerator of the object to an integer value           //
   //                (i.e numeratorval divided by the greatest common divisor) and denominator of //
   //                the object to an integer value(i.e. denominatorval divided by the greatest   //
   //		     common divisor).This division by the greatest common divisor is done to reduce/ 
   //		     the fraction to lowest terms						  //
   //Inputs	    :numeratorval-an integer which specifies the numerator. 			  // 
   //		     denominatorval-an integer which specifies the denominator  		  //
   //Outputs	    :None					   	                          //
   //Local Variables:None  									  //
   //Author	    :Lakshmi Anumolu								  //
   /////////////////////////////////////////////////////////////////////////////////////////////////
  public void getnumdenom(int numeratorval,int denominatorval){
         
        //Call the gcd function to calculate the greatest common divisor of 
	//the input numerator and the denominator
       	int greatestcommondivisor=gcf(numeratorval,denominatorval);
	
	//Reduce the numerator and denominator to the lowest terms.
	numerator=numeratorval/greatestcommondivisor;
	denominator=denominatorval/greatestcommondivisor;
   
  }
      

   ////////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :Rational Addition(Rational r1,Rational r2)				         //
   //Description    :Public function-Addition  which takes in two Rational numbers and provides  //
   //		     the sum of the two numbers 					         //
   //		     Sum of a/b + c/d=(a*d+c*b)/(b*d)                                            // 
   //                Call the gcf function to reduce the sum to its lowest terms                 //
   //Inputs 	    :r1,r2-Instances of Rational class					         //
   //Outputs	    :sum-Instance of Rational class.This contains the sum of the input numbers   //
   //Local Variables:None								         //	
   //Author	    :Lakshmi Anumolu								 //
   ////////////////////////////////////////////////////////////////////////////////////////////////
 
   public Rational Addition(Rational r1,Rational r2){
        
        //Create an instance of Rational-sum-Contains the sum of the input rational numbers
        Rational sum=new Rational();
        
	//sum.numerator contains the numerator-(a*b+b*d)- of the resulting addition.
  	sum.numerator=r1.numerator*r2.denominator + r2.numerator*r1.denominator;
	
	//sum.denominator contains the denominator-(b*d)- of the resulting addition 
	sum.denominator=r1.denominator*r2.denominator;
	
	//Reduce the fraction sum.numerator/sum.denominator to its lowest terms by calling the gcf function
	//Divide the sum.numerator and sum.denominator by the greatest common divisor to get the lowest fraction
	int greatestcommondivisor=gcf(sum.numerator,sum.denominator);
	sum.numerator=sum.numerator/greatestcommondivisor;
	sum.denominator=sum.denominator/greatestcommondivisor;
        
	//return the result-sum- of the addition of 2 rational numbers
	return sum;
   }
 
 
   ///////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :Rational Subtraction(Rational r1,Rational r2)		                //
   //Description    :Public function-Subtraction which takes in two Rational numbers and        //
   //		     provides the difference between the two numbers 			        //		 
   //		     Difference between a/b -c/d=(a*d-c*b)/(b*d)                                //
   //                Call the gcf function to reduce the difference fraction to its lowest terms//
   //Inputs	    :r1,r2-Instances of Rational class					        //
   //Outputs	    :Difference-Instance of Rational class  which holds the difference between  //
   //                the two input rational numbers 				      		//
   //Local Variables:None                                           				//
   //Author	    :Lakshmi Anumolu								//
   ///////////////////////////////////////////////////////////////////////////////////////////////
  
   public Rational Subtraction(Rational r1,Rational r2){
	 //Create an instance of Rational-Difference-Contains the difference between the two input 
         //rational numbers
        Rational Difference=new Rational();

        //Difference.numerator contains the numerator-(a*b-b*d)- of the resulting subtraction.
  	Difference.numerator=r1.numerator*r2.denominator - r2.numerator*r1.denominator;
	
	//Difference.denominator contains the denominator-(b*d)- of the resulting subtraction 
	Difference.denominator=r1.denominator*r2.denominator;
	
	//Reduce the fraction Difference.numerator/Difference.denominator to its lowest terms by 
        //calling the gcf function.Divide the Difference.numerator and Difference.denominator by the
        // greatest common divisor to get the lowest fraction
	int greatestcommondivisor=gcf(Difference.numerator,Difference.denominator);
	Difference.numerator=Difference.numerator/greatestcommondivisor;
	Difference.denominator=Difference.denominator/greatestcommondivisor;

        //return the result-Difference-Contains the difference between the two input 
        //rational numbers
	return Difference;
   }

   ///////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :void Multiplication(Rational r1,Rational r2)		                //
   //Description    :Public function-Multiplication takes in two Rational numbers and           //
   //		     provides the result of mulitiplying  the two numbers 		        //		 
   //		     Multiplication of a/b *c/d=(a*c)/(b*d)				        //
   //Inputs	    :r1,r2-Instances of Rational classes				        //
   //Outputs	    :Mult-Instance of Rational class-which holds the result of multipication of //	
   //                the two input rational numbers                                             //
   //Local Variables:None                                           				//
   //Author	    :Lakshmi Anumolu								//
   ///////////////////////////////////////////////////////////////////////////////////////////////
  
   public Rational Multiplication(Rational r1,Rational r2){
        //Declare an Instance of Rational class-Mult-which holds the result of multipication of 	
        //the two input rational numbers  
        Rational Mult=new Rational();

        //Mult.multnumerator contains the numerator-(a*c)- of the resulting multiplication.
  	Mult.numerator=r1.numerator*r2.numerator;
	
	//Mult.multdenominator contains the denominator-(b*d)- of the resulting multiplication
	Mult.denominator=r1.denominator*r2.denominator;
	
        //Reduce the fraction Mult.numerator/Mult.denominator to its lowest terms by 
        //calling the gcf function.Divide the Mult.numerator and Mult.denominator by the
        // greatest common divisor to get the lowest fraction
	int greatestcommondivisor=gcf(Mult.numerator,Mult.denominator);
	Mult.numerator=Mult.numerator/greatestcommondivisor;
        Mult.denominator=Mult.denominator/greatestcommondivisor;
	
        //return the result-Mult- of the multiplication of 2 rational numbers
	return Mult;
   }
 
 
    ///////////////////////////////////////////////////////////////////////////////////////////////
    //Title	  :void Comparision(Rational r1,Rational r2)			                 //
    //Description :Public function-Comparision takes in two Rational numbers and                 //
    //		   provides the result of comparing  the two numbers	 		         //		 
    //		   Comparision of a/b,c/d ......a/b < c/d if (a*d < (c*b)		         //
    //Inputs	  :r1,r2-Instances of rational class 					         //
    //Outputs	  :None				      					         //
    //Local Variables:None									 //
    //Author	    :Lakshmi Anumolu								 //
    ///////////////////////////////////////////////////////////////////////////////////////////////
  
    public Rational Comparision(Rational r1,Rational r2){
	 	
       	//Check whether the rational number r1 is greater or r2 is greater
         if ((r1.numerator*r2.denominator)<(r2.numerator*r1.denominator)){
		//If the rational number r2 is greater, then return r2
               
	         Rational Max=new Rational(r2.numerator,r2.denominator);
                 return Max;
           }
      else {
	  	//If the rational number r1 is greater, then return r1
	        Rational Max=new Rational(r1.numerator,r1.denominator);
                 return Max;
		
      }
   }		

   
   ///////////////////////////////////////////////////////////////////////////////////////////////////
   //Title	    :void toString(Rational r1)			    			   	    //
   //Description    :Public function-This forms a string with the numerator and denominator of the  //
   //		     input rational number						    	    //
   //		     The string formed is ....numerator + "/" + denominator			    //
   //Inputs	    :r1-instance of Rational class 						    //
   //Outputs        :None									    //
   //Local Variables:None									    //
   //Author	    :Lakshmi Anumolu								    //
   ///////////////////////////////////////////////////////////////////////////////////////////////////
   public void toString(Rational r1){
	
	//return a string containing the numerator and denominator with a "/" symbol in-between the 
	//integers to represent the fraction
	 System.out.println(r1.numerator+"/"+r1.denominator);
   } 



}