Program to compare two fractions

Given two fractions a/b and c/d, compare them and print the larger of the two.

Examples :

Input: 5/6, 11/45
Output: 5/6

Input: 4/5 and 2/3
Output: 4/5

We can simply convert the fractions in floating point values by dividing the numerator by the denominator. Once we have the two floating point numbers corresponding to each fraction, we can compare these numbers and determine which fraction is larger.



However the computed answer may be incorrect due to floating point approximations and truncations during the division process. To get the most accurate answer we should avoid resorting to floating point division.

To compare two fractions we need to make their denominators same. We can do this by cross-multiplying numerators with denominators. Lets see how this works

We have two fractions a/b and c/d.
Let Y = (a/b - c/d) 
      = (ad - bc)/(bd)

Now
if Y > 0 then a/b > c/d 
if Y = 0 then a/b = c/d
if Y < o then a/b < c/d

Since bd is always positive, the sign of Y depends only on the
numerator (ad-bc). So we need to compute (ad-bc) only.

Complexity :
Since we perform two multiplication and one subtraction operation, the answer is computed in constant time i.e O(1)

C++

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// CPP program to find max between
// two Rational numbers
#include <bits/stdc++.h>
using namespace std;
  
struct Fraction {
    int num, den;
};
  
// Get max of the two fractions
Fraction maxFraction(Fraction first, Fraction sec)
{
    // Declare nume1 and nume2 for get the value of
    // first numerator and second numerator
    int a = first.num;
    int b = first.den;
    int c = sec.num;
    int d = sec.den;
  
    // Compute ad-bc
    int Y = a * d - b * c;
  
    return (Y > 0) ? first : sec;
}
  
// Driver Code
int main()
{
    Fraction first = { 3, 2 };
    Fraction sec = { 3, 4 };
  
    Fraction res = maxFraction(first, sec);
    cout << res.num << "/" << res.den;
    return 0;
}

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Java

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// Java program to find max between
// two Rational numbers
  
import java.io.*;
import java.util.*;
  
class Fraction {
      
 int num, den;
  
//Constructor
Fraction(int n,int d){
    num=n;
    den=d;
}
  
 // Get max of the two fractions
static Fraction maxFraction(Fraction first, Fraction sec)
{
    // Declare nume1 and nume2 for get the value of
    // first numerator and second numerator
    int a = first.num;
    int b = first.den;
    int c = sec.num;
    int d = sec.den;
   
    // Compute ad-bc
    int Y = a * d - b * c;
   
    return (Y > 0) ? first : sec;
}
  
// Driver function
public static void main (String[] args) {
  
   Fraction first = new Fraction( 3, 2 );
   Fraction sec = new Fraction( 3, 4 );
   
    Fraction res = maxFraction(first, sec);
    System.out.println(res.num +"/"+ res.den); 
      
}
}
  
// This code is contributed by Gitanjali.

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Python3

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# Python3 program to find max 
# between two Rational numbers
  
# Get max of the two fractions
def maxFraction(first, sec):
      
    # Declare nume1 and nume2 for get the value 
    # of first numerator and second numerator
    a = first[0]; b = first[1]
    c = sec[0]; d = sec[1]
  
    # Compute ad-bc
    Y = a * d - b * c
  
    return first if Y else sec
  
# Driver Code
first = ( 3, 2 )
sec = ( 3, 4 )
res = maxFraction(first, sec)
print(str(res[0]) + "/" + str(res[1]))
  
  
# This code is contributed by Ansu Kumari.

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C#

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// C# program to find max between
// two Rational numbers
using System;
  
class Fraction {
      
    int num, den;
      
    //Constructor
    Fraction(int n,int d)
    {
        num=n;
        den=d;
    }
      
    // Get max of the two fractions
    static Fraction maxFraction(Fraction first, Fraction sec)
    {
        // Declare nume1 and nume2 for get the value of
        // first numerator and second numerator
        int a = first.num;
        int b = first.den;
        int c = sec.num;
        int d = sec.den;
      
        // Compute ad-bc
        int Y = a * d - b * c;
      
        return (Y > 0) ? first : sec;
    }
      
    // Driver function
    public static void Main () 
    {
      
        Fraction first = new Fraction( 3, 2 );
        Fraction sec = new Fraction( 3, 4 );
          
        Fraction res = maxFraction(first, sec);
        Console.WriteLine(res.num +"/"+ res.den); 
          
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP program to find max 
// between two Rational numbers
  
// Get max of the two fractions
function maxFraction($first, $sec)
{
      
    // Declare nume1 and nume2 
    // for get the value of 
    // first numerator and second
    // numerator
    $a = $first[0];
    $b = $first[1];
    $c = $sec[0];
    $d = $sec[1];
  
    // Compute ad-bc
    $Y = $a * $d - $b * $c;
  
    return ($Y) ? $first : $sec;
}
  
// Driver Code
$first = array( 3, 2 );
$sec = array ( 3, 4 );
$res = maxFraction($first, $sec);
echo $res[0] . "/" . $res[1];
  
// This code is contributed 
// by mits.
?>

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Output :

3/2


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Improved By : Mithun Kumar