比较两个分数的程序-yiteyi-C++库

给出两个分数a/b和c/d，比较它们并打印两者中较大的一个。

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例如：

Input: 5/6, 11/45Output: 5/6Input: 4/5 and 2/3Output: 4/5

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

我们可以简单地将分子除以分母，将分数转换成浮点值。一旦我们有了对应于每个分数的两个浮点数，我们就可以比较这些数字并确定哪个分数更大。然而，由于除法过程中的浮点近似和截断，计算出的答案可能不正确。为了得到最准确的答案，我们应该避免使用浮点除法。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交叉相乘来实现。让我们看看这是怎么回事

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/dif Y < o then a/b < c/dSince bd is always positive, the sign of Y depends only on thenumerator (ad-bc). So we need to compute (ad-bc) only.

复杂性： 因为我们执行两次乘法和一次减法运算，所以答案是以恒定时间计算的，即O（1）

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

C++

                         // 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;                       
                         }                       

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.                       

PHP

                         <?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.                       
                         ?>                       

Javascript

                         // javascript 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 > 0) ? first : sec;                       
           
                         }                       
                                   
                         // Driver Code                       
           
                         first = [ 3, 2 ];                       
                         sec = [ 3, 4 ];                       
                         res = maxFraction(first, sec);                       
           
                         document.write(res[0] +                                     "/"                                     + res[1]);                       

输出：

3/2

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