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Find max of two Rational numbers
  • Difficulty Level : Hard
  • Last Updated : 03 Feb, 2020

Given two Rational numbers, the task is to find the maximum of given two rational numbers.

Examples :

Input : first = 3/4, second= 3/2
Output : 3/2

Input : first = 100/100, second = 300/400
Output : 100/100

A simple solution is to find float values and compare the float values. The float computations may cause precision errors. We can avoid them using below approach.

Say first = 3/2, second = 3/4

  • First take a LCM of (4, 2) which is denominator of rational number. so the LCM of this is 4, then divide with both denominator and multiple with numerator of first and second respectively so the denominator value is first numerator = 6, second numerator = 3.
  • Then find the max between these two. so here first numerator is max then print first rational number.

C++




// CPP program to find max between
// two Rational numbers
#include <bits/stdc++.h>
using namespace std;
  
struct Rational
{
    int nume, deno;
};
  
// Get lcm of two number's
int lcm(int a, int b) 
{
    return (a * b) / (__gcd(a, b));
}
  
// Get max rational number
Rational maxRational(Rational first, Rational sec)
{
    // Find the LCM of first->denominator
    // and sec->denominator
    int k = lcm(first.deno, sec.deno);
  
    // Declare nume1 and nume2 for get the value of
    // first numerator and second numerator
    int nume1 = first.nume;
    int nume2 = sec.nume;
  
    nume1 *= k / (first.deno);
    nume2 *= k / (sec.deno);
  
    return (nume2 < nume1)? first : sec;
}
  
// Driver Code
int main()
{
    Rational first = { 3, 2 };
    Rational sec = { 3, 4 };
  
    Rational res = maxRational(first, sec);
    cout << res.nume << "/" << res.deno;
    return 0;
}

Java




// JAVA program to find max between
// two Rational numbers
  
class GFG
{
  
static class Rational
{
    int nume, deno;
  
    public Rational(int nume, int deno) 
    {
        this.nume = nume;
        this.deno = deno;
    }
      
};
  
// Get lcm of two number's
static int lcm(int a, int b) 
{
    return (a * b) / (__gcd(a, b));
}
  
// Get max rational number
static Rational maxRational(Rational first, Rational sec)
{
    // Find the LCM of first.denominator
    // and sec.denominator
    int k = lcm(first.deno, sec.deno);
  
    // Declare nume1 and nume2 for get the value of
    // first numerator and second numerator
    int nume1 = first.nume;
    int nume2 = sec.nume;
  
    nume1 *= k / (first.deno);
    nume2 *= k / (sec.deno);
  
    return (nume2 < nume1)? first : sec;
}
static int __gcd(int a, int b) 
    return b == 0 ? a:__gcd(b, a % b);     
}
  
// Driver Code
public static void main(String[] args)
{
    Rational first = new Rational(3, 2 );
    Rational sec = new Rational(3, 4 );
  
    Rational res = maxRational(first, sec);
    System.out.print(res.nume+ "/" + res.deno);
}
}
  
// This code is contributed by Rajput-Ji

Python




# Python program to find max between 
# two Rational numbers 
import math
  
# Get lcm of two number's 
def lcm(a, b):
      
    return (a * b) // (math.gcd(a, b)) 
  
# Get max rational number 
def maxRational(first, sec):
  
    # Find the LCM of first->denominator 
    # and sec->denominator 
    k = lcm(first[1], sec[1]) 
      
    # Declare nume1 and nume2 for get the value of 
    # first numerator and second numerator 
    nume1 = first[0
    nume2 = sec[0
      
    nume1 *= k // (first[1]) 
    nume2 *= k // (sec[1]) 
      
    return first if (nume2 < nume1) else sec 
  
# Driver Code 
first = [3, 2]
sec = [3, 4]
res = maxRational(first, sec) 
print(res[0], "/", res[1], sep = "")
  
# This code is contributed by SHUBHAMSINGH10

C#




// C# program to find max between
// two Rational numbers
using System;
  
class GFG
{
  
class Rational
{
    public int nume, deno;
  
    public Rational(int nume, int deno) 
    {
        this.nume = nume;
        this.deno = deno;
    }
      
};
  
// Get lcm of two number's
static int lcm(int a, int b) 
{
    return (a * b) / (__gcd(a, b));
}
  
// Get max rational number
static Rational maxRational(Rational first, Rational sec)
{
    // Find the LCM of first.denominator
    // and sec.denominator
    int k = lcm(first.deno, sec.deno);
  
    // Declare nume1 and nume2 for get the value of
    // first numerator and second numerator
    int nume1 = first.nume;
    int nume2 = sec.nume;
  
    nume1 *= k / (first.deno);
    nume2 *= k / (sec.deno);
  
    return (nume2 < nume1)? first : sec;
}
static int __gcd(int a, int b) 
    return b == 0 ? a:__gcd(b, a % b);     
}
  
// Driver Code
public static void Main(String[] args)
{
    Rational first = new Rational(3, 2);
    Rational sec = new Rational(3, 4);
  
    Rational res = maxRational(first, sec);
    Console.Write(res.nume + "/" + res.deno);
}
}
  
// This code is contributed by 29AjayKumar

Output :

3/2

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