两个数的阶乘的GCD-yiteyi-C++库

给定两个数m和n，求其阶乘的GCD。 例如：

null

Input : n = 3, m = 4Output : 6Explanation:Factorial of n = 1 * 2 * 3 = 6Factorial of m = 1 * 2 * 3 * 4 = 24GCD(6, 24) = 6.Input : n = 9, m = 5Output : 20Explanation:Factorial of n = 1 * 2 * 3 *4 * 5 * 6 * 7 * 8 * 9 = 362880Factorial of m = 1 * 2 * 3 * 4 * 5 = 120GCD(362880, 120) = 120

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

A. 简单解决方案 就是找到阶乘这两个数字都有。然后找到 GCD 计算出的阶乘。一 有效解决方案 基于两个阶乘的GCD等于较小的阶乘这一事实（请注意，阶乘具有所有公共项）。下面是上述方法的实现。

C++

                         // CPP program to find GCD of factorial of two                       
                         // numbers.                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         int                                     factorial(                                     int                                     x)                       
                         {                       
                                                 if                                     (x <= 1)                       
                                                 return                                     1;                       
                                                 int                                     res = 2;                       
                                                 for                                     (                                     int                                     i = 3; i <= x; i++)                       
                                                 res = res * i;                       
                                                 return                                     res;                       
                         }                       
           
                         int                                     gcdOfFactorial(                                     int                                     m,                                     int                                     n)                       
                         {                       
                                                 return                                     factorial(min(m, n));                       
                         }                       
           
                         int                                     main()                       
                         {                       
                                                 int                                     m = 5, n = 9;                       
                                                 cout << gcdOfFactorial(m, n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find GCD of factorial                       
                         // of two numbers.                       
                         public                                     class                                     FactorialGCD{                       
                                   
                         static                                     int                                     factorial(                                     int                                     x)                       
                         {                       
                                                 if                                     (x <=                                     1                                     )                       
                                                 return                                     1                                     ;                       
                                                 int                                     res =                                     2                                     ;                       
                                                 for                                     (                                     int                                     i =                                     3                                     ; i <= x; i++)                       
                                                 res = res * i;                       
                                                 return                                     res;                       
                         }                       
           
                         static                                     int                                     gcdOfFactorial(                                     int                                     m,                                     int                                     n)                       
                         {                       
                                                 int                                     min = m < n ? m : n;                       
                                                 return                                     factorial(min);                       
                         }                       
           
                                                 /* Driver program to test above functions */                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     m =                                     5                                     , n =                                     9                                     ;                       
                                   
                                                 System.out.println(gcdOfFactorial(m, n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Prerna Saini                       

python

                         # Python code to find GCD of factorials of                       
                         # two numbers.                       
                         import                                     math                       
           
                         def                                     gcdOfFactorial(m, n) :                       
                                                 return                                     math.factorial(                                     min                                     (m, n))                       
           
                         # Driver code                       
                         m                                     =                                     5                       
                         n                                     =                                     9                       
                         print                                     (gcdOfFactorial(m, n))                       

C#

                         // C# program to find GCD of factorial                       
                         // of two numbers.                       
                         using                                     System;                       
           
                         public                                     class                                     GFG{                       
                                   
                                                 static                                     int                                     factorial(                                     int                                     x)                       
                                                 {                       
                                                 if                                     (x <= 1)                       
                                                 return                                     1;                       
                                   
                                                 int                                     res = 2;                       
                                   
                                                 for                                     (                                     int                                     i = 3; i <= x; i++)                       
                                                 res = res * i;                       
                                   
                                                 return                                     res;                       
                                                 }                       
                                   
                                                 static                                     int                                     gcdOfFactorial(                                     int                                     m,                                     int                                     n)                       
                                                 {                       
                                                 int                                     min = m < n ? m : n;                       
                                                 return                                     factorial(min);                       
                                                 }                       
                                   
                                                 /* Driver program to test above functions */                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                   
                                                 int                                     m = 5, n = 9;                       
                                   
                                                 Console.WriteLine(gcdOfFactorial(m, n));                       
                                                 }                       
                         }                       
                                   
                         // This code is contributed by Anant Agarwal.                       

PHP

                         <?php                       
                         // PHP program to find GCD                       
                         // of factorial of two numbers.                       
           
                         function                                     factorial(                                     $x                                     )                       
                         {                       
                                                 if                                     (                                     $x                                     <= 1)                       
                                                 return                                     1;                       
                                                 $res                                     = 2;                       
                                                 for                                     (                                     $i                                     = 3;                                     $i                                     <=                                     $x                                     ;                                     $i                                     ++)                       
                                                 $res                                     =                                     $res                                     *                                     $i                                     ;                       
                                                 return                                     $res                                     ;                       
                         }                       
           
                         function                                     gcdOfFactorial(                                     $m                                     ,                                     $n                                     )                       
                         {                       
                                                 return                                     factorial(min(                                     $m                                     ,                                     $n                                     ));                       
                         }                       
           
                         // Driver Code                       
                         $m                                     = 5;                                     $n                                     = 9;                       
                         echo                                     gcdOfFactorial(                                     $m                                     ,                                     $n                                     );                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // JavaScript program to find GCD of factorial                       
                         // of two numbers.                       
           
                                                 function                                     factorial(x) {                       
                                                 if                                     (x <= 1)                       
                                                 return                                     1;                       
                                                 var                                     res = 2;                       
                                                 for                                     (i = 3; i <= x; i++)                       
                                                 res = res * i;                       
                                                 return                                     res;                       
                                                 }                       
           
                                                 function                                     gcdOfFactorial(m , n) {                       
                                                 var                                     min = m < n ? m : n;                       
                                                 return                                     factorial(min);                       
                                                 }                       
           
                                                 /* Driver program to test above functions */                       
                                   
                                                 var                                     m = 5, n = 9;                       
           
                                                 document.write(gcdOfFactorial(m, n));                       
           
                         // This code is contributed by aashish1995                       
           
                         </script>                       

输出：

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