程序比较两个分数

给定两个分数a / b和c / d，将它们进行比较并打印两者中较大的一个。

例子 ：

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

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

我们可以通过将分子除以分母来简单地将分数转换为浮点值。一旦有了对应于每个分数的两个浮点数，就可以比较这些数字并确定哪个分数更大。

但是，由于除法过程中的浮点近似和截断，所计算的答案可能不正确。为了获得最准确的答案，我们应避免求助于浮点除法。

为了比较两个分数，我们需要使它们的分母相同。我们可以通过将分子与分母相乘来实现。让我们看看这是如何工作的

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.

复杂度：
由于我们执行两次乘法和一次减法运算，因此答案是在恒定时间内计算的，即O(1)

C++

// CPP program to find max between
// two Rational numbers
#include 
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;
}

Java

// 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.

Python3

# 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.

C#

// 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.

输出 ：

3/2